EXERCISE 83

1. A schoolroom is 32 ft. 8 in. long. Express the length in inches.

2. A room is 282 in. wide. Express the width in feet and inches; in feet and a fraction.

3. How much will a strip of carpet cost at 50 a yard, the strip being 16 ft. 6 in. long?

4. A wheel is 11 ft. in circumference. How many times will it turn in going 2 mi.?

5. If a lot is 197 ft. 9 in. long and 824 ft. wide, the length is how many rods greater than the width?

6. If a man is walking 88 yd. a minute, he is walking at the rate of how many miles per hour?

7. If a cubic inch of cast iron weighs 43% oz., how many pounds does a cubic foot weigh?

8. If a cubic foot of ice weighs 57 lb. 8 oz., how many cubic feet of ice will it take to weigh a ton?

9. The radius of the earth at the equator is estimated to be 20,926,202 ft. Express this in miles and feet.

10. If a pile of wood contains 2760 cu. ft., how many cords does it contain?

11. Express 2 ft. 6 in. as inches; as feet and a common fraction; as feet and a decimal; as a fraction of a yard; as a fraction of a rod.

12. A horse is 14 hands high. Express this in inches; in feet and inches; in feet and a common fraction; in feet and a decimal fraction.

13. A cubic foot of water weighs nearly 1000 oz. How many pounds is this? Express the result in pounds and ounces; in pounds and a common fraction of a pound; in pounds and a decimal fraction of a pound.

14. How many pounds does 5 cu. yd. 18 cu. ft. of earth weigh, if a cubic yard weighs 1 T. 825 lb.?

15. If the average weight of a certain kind of water pipe is 15 lb. 8 oz. per foot, how many feet of the pipe will it take to weigh a ton?

16. If the water in a certain harbor is 14 fathoms deep, a fathom being 6 ft., what is the depth in feet? If the depth is 165 ft., what is the depth in fathoms ?

17. If a man takes 100 steps of 0.8 yd. each in a minute, how long will it take him to walk a distance of 16 mi.?

18. When sound travels 1116 ft. a second, how far distant is the lightning flash (which is seen practically instantaneously) when a man hears the thunder 9 sec. after he sees the flash?

19. If a cubic foot of ice weighs 57 lb. 8 oz., what will be the weight in tons of the mass of ice 1 ft. thick that covers a pond whose surface is 100,000 sq. yd. ?

20. A train leaves Binghamton at 5 min. past 8, and reaches a place 59.6 mi. distant at 5 min. before 10. What is the average time per mile? Answer to two decimal places.

21. A train leaves Albany at 8.45 A.M., and reaches a place 284.74 mi. distant at 3.30 P.M. What is the average time per mile? Answer to two decimal places.

22. On a trip of three miles an automobile required 2 min. 34 sec. for the first mile, 2 min. 17 sec. for the second, and 1 min. 56 sec. for the third. How long did it take for the three miles?

23. When a man was three miles from his railroad station he had 20 min. 30 sec. before his train was due to leave. He then drove one mile in 6 min. 48 sec., and a second mile in 6 min. 54 sec. What is the longest time in which he can drive the last mile and still catch his train?

24. This farmer is pointing to a field that is 80 rd. long and 40 rd. wide. How many square rods does it contain? How many acres?

25. If a field is 80 rd. square, how many acres does it contain? How many acres will it contain if it is 160 rd. square?

26. A man thinks of replacing the fence around a field by a 4-strand barbed wire fence. The field is a rectangle 120 rd. by 30 rd. How many pounds of barbed wire will he need, allowing 1 lb. of barbed wire to the rod ?

27. If an artesian well produces 3.265 cu. ft. of water per minute, and a cubic foot of water weighs 62.5 lb., what is the weight of the water produced in an hour?

28. If a man allows 350 cu. ft. of solidly stacked hay to the ton, how many tons of hay are there in a mow that contains 4375 cu. ft.?

29. If corn fodder loses of its weight in curing, how much will 28 T. of green fodder weigh after it is cured? How much will 45 T. weigh?

30. Taking the annual rainfall of New York as 37.52 in., what will be the weight of water that will fall on 1 sq. ft. of land per year? on 1 sq. rd.? on 1 A.?

31. If a farmer has 64 A. of wheat yielding 24 bu. per acre, what will it cost him for threshing at 4 a bushel?

32. What is the total cost of 15 bu. of wheat at 80%, 17 bu. of potatoes at 28, 13 bu. of corn at 45o, and 21 bu. of oats at 41¢?

33. If a man and team can seed 8 A. a day, how long will it take to seed a field of 96 A., and what will it cost at $6.12 a day?

34. Supposing they are able to plow 2 A. a day, how much will it cost to plow a 76-acre field at $6.12 a day?

35. If three fourths of the weight of potatoes is water, and if a bushel of potatoes weighs 60 lb., what is the weight of water in 275 bu. of potatoes?

36. If two twenty-fifths of the weight of barley is water, and if a bushel of barley weighs 48 lb., what is the weight of water in 275 bu. of barley?

37. When wheat is worth 92 a bushel, what is the value of the wheat grown on 75 A., if the average yield per acre is 22 bu.?

38. If wheat weighs 60 lb. per bushel, and the average yield is 24 bu. per acre, what will be the weight of the wheat grown on a field of 421⁄2 A. ?

39. An experiment has shown that it requires a pull of 92 lb. to draw a ton over a good gravel road, and 2.35 times as much to draw the same load over a common dirt road. What pull is required for the dirt road?

40. It is estimated that a pine pillar of a certain length, and 4 in. square at the base, will support 12.1 T. of the weight of a barn floor. At this rate, how much will such a pillar 4 in. thick and 8 in. wide support? a pillar 4 in. thick and 10 in. wide? a pillar 4 in. thick and 12 in. wide?

151. Advantage of Cancellation. As we have already found, there is often an advantage in stating a problem in a single step, endeavoring then to simplify the work by cancellation.

For example, a man in rapid walking takes 120 steps a minute, averaging 26 in. each. How long will it take him to walk a mile?

Since he walks 26 in. in taking 1 step and takes 120 steps a minute, in 1 min. he will walk 120 x 26 in. Since in 1 mi. there are 5280 ft., or 5280 × 12 in., it will take him as many minutes to walk a mile as 5280 × 12 in. divided by 120 × 26 in. Therefore we have

It will therefore take the man 20 minutes to walk 1 mile.

EXERCISE 84

1. A manufacturer ships 2500 lb. of brass bedsteads from New York to Chicago. Such freight takes the first-class rate, 75¢ per hundred pounds. The manufacturer agrees to pay two thirds of the freight. How much does he pay 7?

2. A manufacturer ships 1800 lb. of iron bedsteads, this kind of freight taking the second-class rate, 65¢ per hundred pounds. He agrees to pay one third of this freight. How much does he pay?

3. A manufacturer ships 650 lb. of furniture casters in boxes, this kind of freight taking the third-class rate, 50¢ per hundred pounds. If he pays three fourths of this freight, how much does he pay?

4. A manufacturer ships 900 lb. of crated bamboo bedsteads, this kind of freight taking double the first-class rate. If the first-class rate is 75 per hundred pounds, how much is the freight?