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PROPORTIONALITY Lesson 18 Section 2 |
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This means that if one of the quantities doubles, then the other will become half as large. For the inverse of the ratio 2 to 1 ("doubles") is the ratio 1 to 2 ("half"). The terms are exchanged. Example 1. Let us suppose that the time it takes to do a job is inversely proportional to the number of workers. The more workers, the shorter the time. Specifically: If 6 workers can do a job in 4 days, then how long will it take 12 workers? Answer. The number of workers has doubled , going from 6 to 12. Therefore it will take only half as many days. It will take only 2 days. Example 2. The speed that a car can achieve in 10 seconds is inversely proportional to its weight. (That is, the more the car weighs, the slower it will be going.) After 10 seconds, a car that weighs 2400 pounds can achieve a speed of 44 miles per hour. If the car weighed 1600 pounds, how fast would it be going? Answer. What ratio has the new weight to the original weight -- 1600 pounds to 2400 pounds? 1600 is two thirds of 2400: 1600 is to 2400 as 16 is to 24 as 2 is to 3. (After ignoring the 0's, we see that both 16 and 24 have a common divisor 8. Lesson 16, Question 7.) Now, the inverse ratio of 2 to 3 is the ratio 3 to 2. And since 3 ÷ 2 = 1 R 1, then 3 is one and a half times 2. The speed therefore will be one and a half times 44: 44 + 22 = 66 miles per hour. When quantities are inversely proportional, we say that one of them varies inversely as the other. Thus the speed that a car can achieve in a given time varies inversely as its weight. Please "turn" the page and do some Problems. or Continue on to the next Lesson. Introduction | Home | Table of Contents Please make a donation to keep TheMathPage online. Copyright © 2001-2007 Lawrence Spector Questions or comments? E-mail: themathpage@nyc.rr.com |
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