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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.