and 7×21 hrs., or 36 hrs., to mow, or the whole field.

Therefore,

A's time = 49 hrs.
B's time = 36 hrs.

EXERCISE 93

1. If a person can do a piece of work in 7 da., what part of the work can he do in one day? If he can do the work in 4 da., what part of the work can he do in one day?

2. If B can copy a manuscript in 5 hr., how much can he copy in 1 hr.?

3. John travels of the distance between two cities in 1 hr. How many hours will it take him to travel the remainder of the distance?

4. A can do a piece of work in 3 hr., B in 5 hr., and C in 5 hr. How long will it take the three working together to do the work?

5. A can do a piece of work in 4 hr., B in 5 hr., and A, B, and C together in 1 hr. How long would it take C alone to do the work?

6. A, B, and C can do a piece of work in 6, 8, and 10 da., respectively. If they begin the work together, what part of the work remains to be done at the end of the second day?

7. A, B, and C can build a fence in 10, 15, and 20 hr. respectively. They work together for 4 hr., when B quits. In what time can A and C finish the work?

8. A cistern has two pipes. One can fill it in 20 min., and the other can empty it in 30 min. If the cistern is

empty, in what time can it be filled, if both pipes begin to flow at the same instant?

MOTION IN THE SAME DIRECTION, OR IN OPPOSITE DIRECTIONS

Example 1. A starts to overtake B, who is 100 yd. ahead of him. A travels 11 yd. to B's 9 yd. How far must A travel in order to overtake B?

SOLUTION. A gains on B 2 yd. in every 11 yd. he goes. .. A gains on B 1 yd. in every 5 yd. he goes.

.. A gains on B 100 yd. in every 550 yd. he goes.

Ans. 550 yd.

Example 2. A freight train moving at the rate of 18 mi. an hour is 78 mi. ahead of a passenger train moving in the same direction at the rate of 30 mi. an hour. Find the distance the passenger train must run to overtake the freight train.

SOLUTION. In 1 hr. the passenger train gains on the freight (3018) mi., i.e. 12 mi.

.. in (78÷12) hr. the passenger train will overtake the freight train, i.e. in 61 hr.

In 6 hr. the passenger train goes 30 mi. x 61= 195 mi.

EXERCISE 94

1. Two ships leave New York for Glasgow, one on Monday morning at 9 o'clock, and the other on the following morning at 9 o'clock. Their rates were 15 and 21 miles an hour respectively. How far from New York City will the second ship overtake the first?

2. Dallas and Galveston are 315 mi. apart. A train leaves Dallas for Galveston at 8 o'clock A.M. at the rate of 30 mi. an hour. At the same time a train leaves Gal

veston for Dallas at the rate of 33 mi. an hour. How far will the trains be from Dallas when they meet?

3. Paris, Texas, is 584 ini. from St. Louis. A passenger train leaves Paris for St. Louis at 6.50 P.M. Three hours later a freight train leaves St. Louis for Paris. When and where will they meet, the rates being respectively 24 mi. and 16 mi. per hour?

4. A man walking at the rate of 4 mi. an hour is overtaken by a train 88 yd. long, and is passed in 10 sec. Find the rate of the train.

5. A train going at the rate of 40 mi. an hour passes in 6 sec. a man walking in the same direction at the rate of 4 mi. an hour. What is the length of the train?

6. Two trains start from the same station and travel in the same direction. The first train leaves at 7 A.M., and the second train at 9 A.M. How many miles from

the station will the second train overtake the first if the rate of the first train is 30 mi. per hour and the rate of the second train is 45 mi. per hour?

REVIEW

EXERCISE 95

1. Multiply the sum of 1,1,1, by 1, and divide the product by

21

332

2. What number taken from 201 leaves as a remainder 42?

3. The difference between two numbers is 12, and the less is 45. Find the other number.

4. Which is the greater, of 44, or 3 of 43 ?

5. From of the sum of,,,, take the sum of

6. From of ( − 1 + §) take († + } − }).

7. Express in pounds the difference between .0125 of a ton and cwt.

8. What fraction having 48 for denominator is equivalent to .1875 ?

9. Find in feet the value of 15 of a mile.

10. Express yd. as the decimal of a rod.

11. Express of 95 lb. as the decimal of 14 cwt.

12. Express 27 lb. as the decimal of a ton.

13. Take T. from 1 T., and express your result in pounds.

14. From of a right angle take 33° 45'.

15. From of a circumference take of the circumference and express your answer in degrees.

16. of a bushel is what part of 1g bu. ?

17. An estate is left to A, B, and C. A gets of the estate, B of the estate, and C the remainder. What part of the estate does C get? If C's share is $450, what is the value of the estate? Find A's share and B's share.

18. A man spends of his salary on board, on clothing, on rent. He saves the remainder, amounting to

19. Subtract from 2.1, and divide the remainder by .25.

20. The dividend is 3.562 and the quotient is .3125. Find the divisor.

21. Express $5.24 as a decimal of $100.

22. After giving away,, and of his money, a man has left $392.95. How much money had he at first?

23. The third part of a number exceeds the fifth part of the same number by 15. What is the number?

24. The sixth part and the eighth part of a number together make 661. What is the number?

25. If and

of a farm are together worth $1650,

what is of the remainder worth?

26. Subtract the product of and 3 from their sum.

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27. What number divided by 33 gives 12 for the quotient?

28. Find the value of 3 of 13 of $19.80.

29. A man owns of a boat and sells of his share for $750. At this rate, find the value of the boat.

30. If 6 men do a piece of work in 9 days, how long will it take 4 men to do the same work?

31. If 15 men pave a street in 16 days, how long will it take 40 men to pave the same street?

32. If 18 men remove an embankment in 12 da., how long will it take 24 men to remove the embankment ?

33. Two trains start at the same time from two stations 840 mi. apart, and travel toward each other, one train going at the rate of 35 mi. an hour, and the other of 25 mi. an hour. In how many hours will they meet?

34. If a man performs of a piece of work in 15 da., in how many days more will he complete the work?

35. Add,,,, and . Express the sum as a decimal. Check by reducing to decimals and adding.

36. What is the smallest number which, added to the sum of,, and §, will make the final result an integer?