Rational Expression Word Problems: Estimate the Costs

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120. Toxic pollutants. The annual cost in dollars for removing
p% of the toxic chemicals from a town's water supply is given by the formula

C(p) = 500,000
_______
100-p

a) Use the accompanying graph to estimate the cost for removing 90% and 95% of the toxic chemicals.
b) Use the formula to find C(99.5) and C(99.9).
c) What happens to the cost as the percentage of pollutants removed approaches 100%?

82. Driving marathon. Felix drove 800 miles in x hours on Monday.
a) Write a rational expression for his average speed.

90. Barn painting. Melanie can paint a certain barn by herself in x days. Her helper Melissa can paint the same barn by herself in 2x days. Write a rational expression for the fraction of the barn that they complete in one day by working together. Evaluate the expression for x = 5

64. Commuting students. At a well-known university, 1/4 of the undergraduate students commute, and 1/3 of the graduate students commute. One-tenth of the undergraduate students drive more than 40 miles daily and 1/6 of the graduate students drive more than 40 miles daily. If there are twice as many undergraduate students as there are graduate students, then what fraction of the commuters drive more than 40 miles daily?

68. Telephoto lens. Use the formula to find the image distance i for an object that is 2,000,000 mm from a 250-mm telephoto lens.

30. Rise and run. If the rise is 3/2 and the run is 5, then what is the ratio of the rise to the run?

46. Fast food. If four out of five doctors prefer fast food, then at a convention of 445 doctors, how many prefer fast food?

50. The golden ratio. The ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was approximately 8 to 5, the golden ratio. If the length of a rectangular painting is 2 ft longer than its width, then for what dimensions would the length and width have the golden ratio?

62. Bear population. To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist's estimate of the size of the bear population?

36. Upstream, downstream. Junior's boat will go 15 miles per hour in still water. If he can go 12 miles downstream in the same amount of time as it takes to go 9 miles upstream, then what is the speed of the current?

54. Big plane. A six-passenger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the wind, then what is the wind speed?

64. Filling a tank. A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank?