Section 6.4

83. Traveling time.  Janet drove 120 miles at x mph before 6:00 A.M. After 6:00 A.M., she increased her speed by 5 mph and drove 195 additional miles. Use the fact that T = D/R to complete the following table. Write a rational expression for her total traveling time. Evaluate the expression for x = 60.

84. Traveling time.  After leaving Moose Jaw, Hanson drove 200 kilometers at x km/hr and then decreased his speed by 20 km/hr and drove 240 additional kilometers. Make a table like the one in Exercise 83. Write a rational expression for his total traveling time. Evaluate the expression for x = 100.

85. House painting.  Kent can paint a certain house by himself in x days. His helper Keith can paint the same house by himself in x = 3 days. Suppose that they work together on the job for 2 days. To complete the table on the next page, use the fact that the work completed is the product of the rate and the time. Write a rational expression for the fraction of the house that they complete by working together for 2 days. Evaluate the expression for x = 6.

86. 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.

Section 6.5

61. Sophomore math.  A survey of college sophomores showed that 5/6 of the males were taking a mathematics class and ¾ of the females were taking a mathematics class. One-third of the males were enrolled in calculus, and 1/5 of the females were enrolled in calculus. If just as many males as females were surveyed, then what fraction of the surveyed students taking mathematics were enrolled in calculus? Rework this problem assuming that the number of females in the survey was twice the number of males.

62. Commuting students.  At a well-known university, ¼ 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?

Section 6.6

63. Lens equation. The focal length f for a camera lens is related to the object distance o and the image distance i by the formula 1/f = 1/o + 1/i. See the accompanying figure. The image is in focus at distance i from the lens. For an object that is 600 mm from a 50-mm lens, use f = 50 mm and o = 600 mm to find i.

64. Telephoto lens.  Use the formula from Exercise 63 to find the image distance i for an object that is 2,000,000 mm from a 250-mm telephoto lens.

Section 6.7

17. Men and women.  Find the ratio of men to women in a bowling league containing 12 men and 8 women.

18. Coffee drinkers.  Among 100 coffee drinkers, 36 said that they preferred their coffee black and the rest did not prefer their coffee black. Find the ratio of those who prefer black coffee to those who prefer nonblack coffee.

19. Smokers.  A life insurance company found that among its last 200 claims, there were six dozen smokers. What is the ratio of smokers to nonsmokers in this group of claimants?

20. Hits and misses.  A woman threw 60 darts and hit the target a dozen times. What is her ratio of hits to misses?

21. While watching television for one week, a consumer group counted 1240 acts of violence and
40 acts of kindness. What is the violence to kindness ratio for television, according to this group?

22. Length to width. What is the ratio of length to width for the rectangle shown?

23. Rise to run.  What is the ratio of rise to run for the stairway shown in the figure?

39. New shows and reruns.  The ratio of new shows to reruns on cable TV is 2 to 27. If Frank counted only eight new shows one evening, then how many reruns were there?

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

41. Voting.  If 220 out of 500 voters surveyed said that they would vote for the incumbent, then how many votes could the incumbent expect out of the 400,000 voters in the state?

42. New product. A taste test with 200 randomly selected people found that only three of them said that they would buy a box of new Sweet Wheats cereal. How many boxes could the manufacturer expect to sell in a country of 280 million people?

43. Basketball blowout.  As the final buzzer signaled the end of the basketball game, the Lions were 34 points ahead of the Tigers. If the Lions scored 5 points for every 3 scored by the Tigers, then what was the final score?

44. 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?

45. Automobile sales. The ratio of sports cars to luxury cars sold in Wentworth one month was 3 to 2. If 20 more sports cars were sold than luxury cars, then how many of each were sold that month?

46. Foxes and rabbits.  The ratio of foxes to rabbits in the Deerfield Forest Preserve is 2 to 9. If there are 35 fewer foxes than rabbits, then how many of each are there?

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