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Section 2.6 #15: The time t required to drive a fixed distance varies inversely as the speed r. It takes 5 hr at a speed of 80 kmhr to drive the fixed distance. How long will it take to drive the same distance at a speed of 70 kmhr?
Solution: From the first sentence we know the following equation holds for some k: t=kr. Plugging in t=5 and r=80 we get the qeuation 5=k80, so we may solve for k by multiplying by 80 to get 400=k. This means t=400r. We are asked to find t given that r=70. To do this plug in r=70 into the equation to see that t=40070hr.
Section 2.6 #17: The maximum number of grams of a fat that should be in a diet varies directly as a person's weight. A person weighing 120 lb should have no more than 60 g of fat per day. What is the maximum daily fat intake for a person weighing 180 lb?
Solution: Let G denote the number of grams of fat and let W denote weight. From the first sentence we get the equation, for some k, G=kW. Plugging in G=60 and W=120 yields 60=120k, and solving for k yields k=60120=12. Therefore the equation is G=W2. To answer the question, we plug in W=180 to get G=1802=90, so a 180 lb person should eat at most 90 grams of fat in a day.