{"id":4634,"date":"2020-04-21T00:19:12","date_gmt":"2020-04-21T00:19:12","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/proportions-and-rates\/"},"modified":"2021-03-22T20:53:35","modified_gmt":"2021-03-22T20:53:35","slug":"proportions-and-rates","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/nwfsc-mathforliberalartscorequisite\/chapter\/proportions-and-rates\/","title":{"raw":"Proportions and Rates","rendered":"Proportions and Rates"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Write a proportion to express a rate or ratio<\/li>\r\n \t<li>Solve a proportion for an unknown<\/li>\r\n<\/ul>\r\n<\/div>\r\nIf you wanted to power the city of Lincoln, Nebraska using wind power, how many wind\u00a0turbines would you need to install? Questions like these can be answered using rates and proportions.\r\n\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14205401\/wind-364996_1280.jpg\"><img class=\"aligncenter wp-image-497\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14205401\/wind-364996_1280-1024x685.jpg\" alt=\"two wind turbines in a field of flowers and low trees\" width=\"613\" height=\"410\" \/><\/a>\r\n<div class=\"textbox\">\r\n<h2>RATES<\/h2>\r\nA rate is the ratio (fraction) of two quantities.\r\n\r\nA <strong>unit rate<\/strong> is a rate with a denominator of one.\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Recall Reducing Fractions<\/h3>\r\nThe Equivalent Fractions Property states that\r\n\r\nIf [latex]a,b,c[\/latex] are numbers where [latex]b\\ne 0,c\\ne 0[\/latex], then\r\n\r\n[latex]{\\dfrac{a\\cdot c}{b\\cdot c}}={\\dfrac{a}{b}}[\/latex].\r\n\r\nEx. [latex]\\dfrac{500}{20}=\\dfrac{25\\cdot 20}{1\\cdot 20}=\\dfrac{25}{1}=25[\/latex]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nYour car can drive 300 miles on a tank of 15 gallons. Express this as a rate.\r\n[reveal-answer q=\"378596\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"378596\"]\r\n\r\nExpressed as a rate, [latex]\\displaystyle\\frac{300\\text{ miles}}{15\\text{ gallons}}[\/latex]. We can divide to find a unit rate:[latex]\\displaystyle\\frac{20\\text{ miles}}{1\\text{ gallon}}[\/latex], which we could also write as [latex]\\displaystyle{20}\\frac{\\text{miles}}{\\text{gallon}}[\/latex], or just 20 miles per gallon.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox\">\r\n<h2>Proportion Equation<\/h2>\r\nA proportion equation is an equation showing the equivalence of two rates or ratios.\r\n\r\nFor an overview on rates and proportions, using the examples on this page, view the following video.\r\n\r\nhttps:\/\/youtu.be\/aZrio6ztHKE\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Using Variables to represent unknowns<\/h3>\r\nRecall that we can use letters we call <strong>variables\u00a0<\/strong>to \"stand in\" for unknown quantities. Then we can use the properties of equality to isolate the variable on one side of the equation. Once we have accomplished that, we say that we have \"solved the equation for the variable.\"\r\n\r\nIn the example below, you are asked to solve the proportion (an equality given between two fractions) for the unknown value [latex]x[\/latex].\r\n\r\nEx. Solve the proportion [latex]\\dfrac{7}{3}=\\dfrac{x}{15}[\/latex]\r\n<p style=\"padding-left: 30px\">We see that the variable we wish to isolate is being divided by 15. We can reverse that by multiplying on both sides by 15.<\/p>\r\n<p style=\"padding-left: 30px\">[latex]\\dfrac{7}{3}=\\dfrac{x}{15}[\/latex]<\/p>\r\n<p style=\"padding-left: 30px\">[latex]15\\cdot \\dfrac{7}{3}=x[\/latex], giving [latex]x=35[\/latex].<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSolve the proportion [latex]\\displaystyle\\frac{5}{3}=\\frac{x}{6}[\/latex] for the unknown value <em>x<\/em>.\r\n[reveal-answer q=\"737915\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"737915\"]This proportion is asking us to find a fraction with denominator 6 that is equivalent to the fraction[latex]\\displaystyle\\frac{5}{3}[\/latex]. We can solve this by multiplying both sides of the equation by 6, giving\u00a0[latex]\\displaystyle{x}=\\frac{5}{3}\\cdot6=10[\/latex].[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nA map scale indicates that \u00bd inch on the map corresponds with 3 real miles. How many miles apart are two cities that are [latex]\\displaystyle{2}\\frac{1}{4}[\/latex] inches apart on the map?\r\n[reveal-answer q=\"439949\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"439949\"]\r\nWe can set up a proportion by setting equal two [latex]\\displaystyle\\frac{\\text{map inches}}{\\text{real miles}}[\/latex]\u00a0rates, and introducing a variable, <em>x<\/em>, to represent the unknown quantity\u2014the mile distance between the cities.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>[latex]\\displaystyle\\frac{\\frac{1}{2}\\text{map inch}}{3\\text{ miles}}=\\frac{2\\frac{1}{4}\\text{map inches}}{x\\text{ miles}}[\/latex]<\/td>\r\n<td>Multiply both sides by <em>x\u00a0<\/em>and rewriting the mixed number<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\displaystyle\\frac{\\frac{1}{2}}{3}\\cdot{x}=\\frac{9}{4}[\/latex]<\/td>\r\n<td>Multiply both sides by 3<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\displaystyle\\frac{1}{2}x=\\frac{27}{4}[\/latex]<\/td>\r\n<td>Multiply both sides by 2 (or divide by \u00bd)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\displaystyle{x}=\\frac{27}{2}=13\\frac{1}{2}\\text{ miles}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nMany proportion problems can also be solved using <strong>dimensional analysis<\/strong>, the process of multiplying a quantity by rates to change the units.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nYour car can drive 300 miles on a tank of 15 gallons. How far can it drive on 40 gallons?\r\n[reveal-answer q=\"526887\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"526887\"]\r\n\r\nWe could certainly answer this question using a proportion: [latex]\\displaystyle\\frac{300\\text{ miles}}{15\\text{ gallons}}=\\frac{x\\text{ miles}}{40\\text{ gallons}}[\/latex].\r\n\r\nHowever, we earlier found that 300 miles on 15 gallons gives a rate of 20 miles per gallon. If we multiply the given 40 gallon quantity by this rate, the <em>gallons<\/em> unit \u201ccancels\u201d and we\u2019re left with a number of miles:\r\n\r\n[latex]\\displaystyle40\\text{ gallons}\\cdot\\frac{20\\text{ miles}}{\\text{gallon}}=\\frac{40\\text{ gallons}}{1}\\cdot\\frac{20\\text{ miles}}{\\text{gallons}}=800\\text{ miles}[\/latex]\r\n\r\nNotice if instead we were asked \u201chow many gallons are needed to drive 50 miles?\u201d we could answer this question by inverting the 20 mile per gallon rate so that the <em>miles<\/em> unit cancels and we\u2019re left with gallons:\r\n\r\n[latex]\\displaystyle{50}\\text{ miles}\\cdot\\frac{1\\text{ gallon}}{20\\text{ miles}}=\\frac{50\\text{ miles}}{1}\\cdot\\frac{1\\text{ gallon}}{20\\text{ miles}}=\\frac{50\\text{ gallons}}{20}=2.5\\text{ gallons}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\nA worked example of this last question can be found in the following video.\r\n\r\nhttps:\/\/youtu.be\/jYwi3YqP0Wk\r\n\r\n<\/div>\r\nNotice that with the miles per gallon example, if we double the miles driven, we double the gas used. Likewise, with the map distance example, if the map distance doubles, the real-life distance doubles. This is a key feature of proportional relationships, and one we must confirm before assuming two things are related proportionally.\r\n\r\nYou have likely encountered distance, rate, and time problems in the past. This is likely because they are easy to visualize and most of us have experienced them first hand. In our next example, we will solve distance, rate and time problems that will require us to change the units that the distance or time is measured in.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nA bicycle is traveling at 15 miles per hour. How many feet will it cover in 20 seconds?\r\n[reveal-answer q=\"946318\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"946318\"]\r\n\r\nTo answer this question, we need to convert 20 seconds into feet. If we know the speed of the bicycle in feet per second, this question would be simpler. Since we don\u2019t, we will need to do additional unit conversions. We will need to know that 5280 ft = 1 mile. We might start by converting the 20 seconds into hours:\r\n\r\n[latex]\\displaystyle{20}\\text{ seconds}\\cdot\\frac{1\\text{ minute}}{60\\text{ seconds}}\\cdot\\frac{1\\text{ hour}}{60\\text{ minutes}}=\\frac{1}{180}\\text{ hour}[\/latex]\r\n\r\nNow we can multiply by the 15 miles\/hr\r\n\r\n[latex]\\displaystyle\\frac{1}{180}\\text{ hour}\\cdot\\frac{15\\text{ miles}}{1\\text{ hour}}=\\frac{1}{12}\\text{ mile}[\/latex]\r\n\r\nNow we can convert to feet\r\n\r\n[latex]\\displaystyle\\frac{1}{12}\\text{ mile}\\cdot\\frac{5280\\text{ feet}}{1\\text{ mile}}=440\\text{ feet}[\/latex]\r\n\r\nWe could have also done this entire calculation in one long set of products:\r\n\r\n[latex]\\displaystyle20\\text{ seconds}\\cdot\\frac{1\\text{ minute}}{60\\text{ seconds}}\\cdot\\frac{1\\text{ hour}}{60\\text{ minutes}}=\\frac{15\\text{ miles}}{1\\text{ miles}}=\\frac{5280\\text{ feet}}{1\\text{ mile}}=\\frac{1}{180}\\text{ hour}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\nView the following video to see this problem worked through.\r\n\r\nhttps:\/\/youtu.be\/fyOcLcIVipM\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]17454[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Write a proportion to express a rate or ratio<\/li>\n<li>Solve a proportion for an unknown<\/li>\n<\/ul>\n<\/div>\n<p>If you wanted to power the city of Lincoln, Nebraska using wind power, how many wind\u00a0turbines would you need to install? Questions like these can be answered using rates and proportions.<\/p>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14205401\/wind-364996_1280.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-497\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14205401\/wind-364996_1280-1024x685.jpg\" alt=\"two wind turbines in a field of flowers and low trees\" width=\"613\" height=\"410\" \/><\/a><\/p>\n<div class=\"textbox\">\n<h2>RATES<\/h2>\n<p>A rate is the ratio (fraction) of two quantities.<\/p>\n<p>A <strong>unit rate<\/strong> is a rate with a denominator of one.<\/p>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Recall Reducing Fractions<\/h3>\n<p>The Equivalent Fractions Property states that<\/p>\n<p>If [latex]a,b,c[\/latex] are numbers where [latex]b\\ne 0,c\\ne 0[\/latex], then<\/p>\n<p>[latex]{\\dfrac{a\\cdot c}{b\\cdot c}}={\\dfrac{a}{b}}[\/latex].<\/p>\n<p>Ex. [latex]\\dfrac{500}{20}=\\dfrac{25\\cdot 20}{1\\cdot 20}=\\dfrac{25}{1}=25[\/latex]<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Your car can drive 300 miles on a tank of 15 gallons. Express this as a rate.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q378596\">Show Solution<\/span><\/p>\n<div id=\"q378596\" class=\"hidden-answer\" style=\"display: none\">\n<p>Expressed as a rate, [latex]\\displaystyle\\frac{300\\text{ miles}}{15\\text{ gallons}}[\/latex]. We can divide to find a unit rate:[latex]\\displaystyle\\frac{20\\text{ miles}}{1\\text{ gallon}}[\/latex], which we could also write as [latex]\\displaystyle{20}\\frac{\\text{miles}}{\\text{gallon}}[\/latex], or just 20 miles per gallon.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox\">\n<h2>Proportion Equation<\/h2>\n<p>A proportion equation is an equation showing the equivalence of two rates or ratios.<\/p>\n<p>For an overview on rates and proportions, using the examples on this page, view the following video.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Basic rates and proportions\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/aZrio6ztHKE?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Using Variables to represent unknowns<\/h3>\n<p>Recall that we can use letters we call <strong>variables\u00a0<\/strong>to &#8220;stand in&#8221; for unknown quantities. Then we can use the properties of equality to isolate the variable on one side of the equation. Once we have accomplished that, we say that we have &#8220;solved the equation for the variable.&#8221;<\/p>\n<p>In the example below, you are asked to solve the proportion (an equality given between two fractions) for the unknown value [latex]x[\/latex].<\/p>\n<p>Ex. Solve the proportion [latex]\\dfrac{7}{3}=\\dfrac{x}{15}[\/latex]<\/p>\n<p style=\"padding-left: 30px\">We see that the variable we wish to isolate is being divided by 15. We can reverse that by multiplying on both sides by 15.<\/p>\n<p style=\"padding-left: 30px\">[latex]\\dfrac{7}{3}=\\dfrac{x}{15}[\/latex]<\/p>\n<p style=\"padding-left: 30px\">[latex]15\\cdot \\dfrac{7}{3}=x[\/latex], giving [latex]x=35[\/latex].<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Solve the proportion [latex]\\displaystyle\\frac{5}{3}=\\frac{x}{6}[\/latex] for the unknown value <em>x<\/em>.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q737915\">Show Solution<\/span><\/p>\n<div id=\"q737915\" class=\"hidden-answer\" style=\"display: none\">This proportion is asking us to find a fraction with denominator 6 that is equivalent to the fraction[latex]\\displaystyle\\frac{5}{3}[\/latex]. We can solve this by multiplying both sides of the equation by 6, giving\u00a0[latex]\\displaystyle{x}=\\frac{5}{3}\\cdot6=10[\/latex].<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>A map scale indicates that \u00bd inch on the map corresponds with 3 real miles. How many miles apart are two cities that are [latex]\\displaystyle{2}\\frac{1}{4}[\/latex] inches apart on the map?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q439949\">Show Solution<\/span><\/p>\n<div id=\"q439949\" class=\"hidden-answer\" style=\"display: none\">\nWe can set up a proportion by setting equal two [latex]\\displaystyle\\frac{\\text{map inches}}{\\text{real miles}}[\/latex]\u00a0rates, and introducing a variable, <em>x<\/em>, to represent the unknown quantity\u2014the mile distance between the cities.<\/p>\n<table>\n<tbody>\n<tr>\n<td>[latex]\\displaystyle\\frac{\\frac{1}{2}\\text{map inch}}{3\\text{ miles}}=\\frac{2\\frac{1}{4}\\text{map inches}}{x\\text{ miles}}[\/latex]<\/td>\n<td>Multiply both sides by <em>x\u00a0<\/em>and rewriting the mixed number<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\displaystyle\\frac{\\frac{1}{2}}{3}\\cdot{x}=\\frac{9}{4}[\/latex]<\/td>\n<td>Multiply both sides by 3<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\displaystyle\\frac{1}{2}x=\\frac{27}{4}[\/latex]<\/td>\n<td>Multiply both sides by 2 (or divide by \u00bd)<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\displaystyle{x}=\\frac{27}{2}=13\\frac{1}{2}\\text{ miles}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Many proportion problems can also be solved using <strong>dimensional analysis<\/strong>, the process of multiplying a quantity by rates to change the units.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Your car can drive 300 miles on a tank of 15 gallons. How far can it drive on 40 gallons?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q526887\">Show Solution<\/span><\/p>\n<div id=\"q526887\" class=\"hidden-answer\" style=\"display: none\">\n<p>We could certainly answer this question using a proportion: [latex]\\displaystyle\\frac{300\\text{ miles}}{15\\text{ gallons}}=\\frac{x\\text{ miles}}{40\\text{ gallons}}[\/latex].<\/p>\n<p>However, we earlier found that 300 miles on 15 gallons gives a rate of 20 miles per gallon. If we multiply the given 40 gallon quantity by this rate, the <em>gallons<\/em> unit \u201ccancels\u201d and we\u2019re left with a number of miles:<\/p>\n<p>[latex]\\displaystyle40\\text{ gallons}\\cdot\\frac{20\\text{ miles}}{\\text{gallon}}=\\frac{40\\text{ gallons}}{1}\\cdot\\frac{20\\text{ miles}}{\\text{gallons}}=800\\text{ miles}[\/latex]<\/p>\n<p>Notice if instead we were asked \u201chow many gallons are needed to drive 50 miles?\u201d we could answer this question by inverting the 20 mile per gallon rate so that the <em>miles<\/em> unit cancels and we\u2019re left with gallons:<\/p>\n<p>[latex]\\displaystyle{50}\\text{ miles}\\cdot\\frac{1\\text{ gallon}}{20\\text{ miles}}=\\frac{50\\text{ miles}}{1}\\cdot\\frac{1\\text{ gallon}}{20\\text{ miles}}=\\frac{50\\text{ gallons}}{20}=2.5\\text{ gallons}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>A worked example of this last question can be found in the following video.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Proportions using dimensional analysis\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/jYwi3YqP0Wk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<p>Notice that with the miles per gallon example, if we double the miles driven, we double the gas used. Likewise, with the map distance example, if the map distance doubles, the real-life distance doubles. This is a key feature of proportional relationships, and one we must confirm before assuming two things are related proportionally.<\/p>\n<p>You have likely encountered distance, rate, and time problems in the past. This is likely because they are easy to visualize and most of us have experienced them first hand. In our next example, we will solve distance, rate and time problems that will require us to change the units that the distance or time is measured in.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>A bicycle is traveling at 15 miles per hour. How many feet will it cover in 20 seconds?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q946318\">Show Solution<\/span><\/p>\n<div id=\"q946318\" class=\"hidden-answer\" style=\"display: none\">\n<p>To answer this question, we need to convert 20 seconds into feet. If we know the speed of the bicycle in feet per second, this question would be simpler. Since we don\u2019t, we will need to do additional unit conversions. We will need to know that 5280 ft = 1 mile. We might start by converting the 20 seconds into hours:<\/p>\n<p>[latex]\\displaystyle{20}\\text{ seconds}\\cdot\\frac{1\\text{ minute}}{60\\text{ seconds}}\\cdot\\frac{1\\text{ hour}}{60\\text{ minutes}}=\\frac{1}{180}\\text{ hour}[\/latex]<\/p>\n<p>Now we can multiply by the 15 miles\/hr<\/p>\n<p>[latex]\\displaystyle\\frac{1}{180}\\text{ hour}\\cdot\\frac{15\\text{ miles}}{1\\text{ hour}}=\\frac{1}{12}\\text{ mile}[\/latex]<\/p>\n<p>Now we can convert to feet<\/p>\n<p>[latex]\\displaystyle\\frac{1}{12}\\text{ mile}\\cdot\\frac{5280\\text{ feet}}{1\\text{ mile}}=440\\text{ feet}[\/latex]<\/p>\n<p>We could have also done this entire calculation in one long set of products:<\/p>\n<p>[latex]\\displaystyle20\\text{ seconds}\\cdot\\frac{1\\text{ minute}}{60\\text{ seconds}}\\cdot\\frac{1\\text{ hour}}{60\\text{ minutes}}=\\frac{15\\text{ miles}}{1\\text{ miles}}=\\frac{5280\\text{ feet}}{1\\text{ mile}}=\\frac{1}{180}\\text{ hour}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>View the following video to see this problem worked through.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Proportions with unit conversion\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/fyOcLcIVipM?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm17454\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=17454&theme=oea&iframe_resize_id=ohm17454&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-4634\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Problem Solving. <strong>Authored by<\/strong>: David Lippman. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\">http:\/\/www.opentextbookstore.com\/mathinsociety\/<\/a>. <strong>Project<\/strong>: Math in Society. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>wind-364996_1280. <strong>Authored by<\/strong>: Stevebidmead. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/pixabay.com\/en\/wind-turbines-farmland-364996\/\">https:\/\/pixabay.com\/en\/wind-turbines-farmland-364996\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/cc0\">CC0: No Rights Reserved<\/a><\/em><\/li><li>Basic rates and proportions. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/aZrio6ztHKE\">https:\/\/youtu.be\/aZrio6ztHKE<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Proportions using dimensional analysis. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/jYwi3YqP0Wk\">https:\/\/youtu.be\/jYwi3YqP0Wk<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Proportions with unit conversion. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/fyOcLcIVipM\">https:\/\/youtu.be\/fyOcLcIVipM<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Considering how\/if things scale. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/-e2typcrhLE\">https:\/\/youtu.be\/-e2typcrhLE<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Comparing quantities involving large numbers. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located 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