Subtract, but do not copy:

(Time for these 12 examples is less than 4 minutes.)

12.

13.

14.

15.

11. 16. 874,362 487,398 687,481 768,042 488,398 763,904 439,728 248,099 298,385 38,098 298,468 498,927

17. 18. 19. 20. 21. 22. 249,763 863,901 848,729 511,872 863,784 948,728 152,948 248,763 385,621 355,902 497,687 349,875

Add, but do not copy:

(Time for these 6 examples is less than 4 minutes.)

(Time for these 6 examples is less than 4 minutes.)

Time for these 8 examples is less than 4 minutes.)

The average man engaged in any occupation can, in one hour, do a certain amount of work; in two hours he can do twice that amount of work, or as much work as two men can do in one hour; thus, it naturally follows that when a piece of work can be done, for instance, by 10 men in 6 hours, the total time consumed by the 10 men in doing this work is the same as 60 hours of one man's work; in other words, the work requires 60 "man-hours," a "man-hour" being 1 man's effort for 1 hour of time.

The number of "man-hours" required for any piece of work is the product of the number of men engaged on the work multiplied by the number of hours consumed in doing the work.

When the number of "man-hours" necessary for a piece of work is known, we find either the number of men to be engaged or the number of hours to be consumed, by dividing the number of "man-hours" by

the known factor; thus, a piece of work which can be completed in 24 man-hours, can be done by 1 man in 24 hours, by 2 men in 12 hours, by 3 men in 8 hours, by 4 men in 6 hours, by 6 men in 4 hours, by 8 men in 3 hours, by 12 men in 2 hours, or by 24 men in 1 hour.

Another "special working unit" in common use in railroading is the "ton-mile"; this is the equivalent of hauling 1 ton a distance of 1 mile. The number of tons hauled multiplied by the number of miles they are hauled equals the "ton-miles."

There are many other "special working units," such as the "kilowatt-hour," the "foot-pound," the "lightyear," the "acre-inch," etc., all based on the same general principle of using the product of two units of

measure.

Exercise 23-Oral.

1. When a certain piece of work can be completed by 2 men in 1 hour, how long would it take 1 man to do the work? How many man-hours are needed to do this work?

2. How many man-hours are needed to do a certain job, if 10 men can do it in 10 hours?

3. To build a certain wall, 5 men worked 8 hours

each and 5 other men worked 12 hours each; how many man-hours were needed to build this wall?

4. To plow a certain field, 48 man-hours of work were required; how many men should be engaged to finish this work in 8 hours? In 6 hours? In 4 hours?

5. To dig a certain trench, 36 man-hours of work

were required; how quickly can 3 men dig this trench? 4 men? 6 men? 9 men? 12 men? 18 men? 24 men?

6. A freight engine had to haul 400 tons of freight 2 miles to place it on a side-track; how many ton-miles were involved in this operation?

7. If the cost of moving machinery by freight is 10¢ per ton-mile, what is the cost of moving 10 tons 10 miles?

8. The electrical energy required to keep 1 electric lamp burning 50 hours is equal to that required to keep 10 lamps burning for how many hours? 9. At 1¢ per lamp per hour, what is the cost of burning 6 lamps 5 hours?

10. Could the burning of 1 lamp for 1 hour be called a lamp-hour?

11. Tell in good English what is meant by a man-hour. 12. Tell in good English what is meant by a ton-mile.

Exercise 24-Written.

Be this manufacturer for to-day.

1. You estimated that it would require 1,500 manhours to execute a contract for steel rails and you had only 10 working days in which to do the work; if your men worked 7 hours per day, how many men were needed?

2. A contractor who works for you has a weekly pay

roll amounting to $720.00; if his men work 40 hours per week and the rate is 60¢ per manhour, how many men has he?

3. In one department of your business 35 men are paid a total of $2,520. for working 3 weeks of 48 hours each; what is the rate of wages per man-hour?

4. The weekly pay roll in another department amounts to $1,108.80; if the rate per man-hour is 55¢ and there are 48 men employed, how many hours per week do they work?

5. If 1,050 tons of your freight are hauled 250 miles at a cost of 1 per ton-mile, what is the total cost?

6. A contractor agreed to build an addition to your factory in 16 weeks and estimated that the work would require 76,800 man-hours; being unable to furnish more than 50 men with the necessary tocls and machinery, he decided to work two shifts of 50 men each-a day shift and a night shift. If the day shift worked 9 hours per day 6 days a week, how many hours per day for 6 days a week did the night shift work?