5. In fishing John held the large end of the pole sta

tionary in the left hand.

The right hand was 2 ft. 9 ins.

farther up the pole, which was 12 ft. long. With his right hand it took a force of 8 ozs. to sustain the fish. What did it weigh?

Draw a diagram to aid in solving this problem.

6. In drawing a nail with a hammer the distance from the fulcrum to the nail is 2 ins., from fulcrum to hands is 11 ins. How much direct pull is exerted upon the nail if it requires 95 lbs. of pull

upon the hammer handle to extract it?

7. A boy weighing 96 lbs. is swinging on a gate, having 2 hinges, 12 ft. from the hinges. It is 3 ft. 4 ins. from one hinge to the other. How much pull does the

boy's weight exert upon the upper hinge? How much does it push upon the lower hinge? Draw a diagram before attempting to solve. Compare with the last problem.

8. Two men carry a weight of 195 lbs. suspended on a pole between them. If the weight is 6 ft. from one man and 9 ft. from the other, how many pounds does each carry? In order that one may carry of the weight where must the weight be hung?

COMPOUND PROPORTION

441. If 18 men working 6 hrs. per day can dig a canal 50 ft. long in 25 days, how many men working 10 hrs. per day can dig a canal 80 ft. long in 8 days?

This problem can be separated into simple proportions and solved as follows:

If 18 men can dig a canal in 25 days, how many men are required to dig the same canal in 8 days? This is expressed in proportion. (1) Solving, we get 225 men. The canal is, how

previous statements have been made under the assumption that the men were to work 6 hrs. per day instead of 10 hrs. If 90 men can dig a canal 80 ft. long in 8 days, working 7 hrs. per day, how many men will be required to dig a canal 80 ft. long in 8 days, working 10 hrs. per day? This is stated in proportion. (3) Solving, we get 54 men, which is the final answer. This method of procedure may be shortened. Multiplying the completed proportions, 1, 2, and 3 together, term by term, we obtain a new proportion, which, expressed as a ratio, is shown in 4. We see that the answers obtained from the first two proportions cancel, leaving the second member a simple ratio. The ratio may now be expressed as a proportion, as is shown in 5, and solved, as follows:

The fact that the first two answers cancel shows that it was unnecessary to obtain them to arrive at the final answer.

RULE 1. Place the unknown quantity as the fourth term of the proportion.

2. Place as the third term of the proportion the quantity given in the problem expressing the same kind of thing as the unknown quantity.

3. Take each of the other ratios separately, and arrange according to their relation to the ratio already stated.

4. The product of all the means divided by the product of all the extremes, except the unknown one, will give the

answer.

442. The product of two or more simple ratios is a Compound Ratio.

443. A proportion in which either or both ratios are compound is a Compound Proportion.

EXERCISE 245,- WRITTEN

1. If 17 men working 7 hrs. a day can build a bridge in 22 days, how many men working 10 hrs. a day will it take to build the bridge in 4 days?

2. If 3 men can milk 35 cows in 1.5 hrs., how many men will it take to milk 65 cows in hr.?

3. If 3 teams working 5 hrs. a day can haul dirt as fast as 5 men can excavate it, how many teams working 7 hrs. a day are required to haul dirt as fast as 15 men can excavate it?

4. If 6 men can draw and house 32 tons of hay in 2 days, how many men are needed to draw and house 14

tons in 6 hrs. ?

5. If 2 men cut 8 cords of wood in 4 days, how long will it take 12 men to cut 36 cords?

6. If 4 men with a one-horse plow break 28 acres in 7 days, how many days will it take 3 men with two-horse plows (a man with a two-horse plow doing twice as much work as a man with a one-horse plow) to break 42 acres?

7. If the eggs laid by 28 hens in 16 weeks are worth $32.50, what will be the value of the eggs laid by 50 hens in 12 weeks?

8. If it requires 35 cows giving 77 qts. of milk each, per week, to supply 425 customers, how many cows giving 270 qts. per month will be required to supply 125 customers?

9. If 30 cows give 462 lbs. of milk in 21 days, how many cows are required to give 1200 lbs. in 7 days?

10. If 4320 lbs. of silage last 30 cows 48 days, how much silage is needed for 15 cows for 60 days?

11. If the contents of a tank of water 2 × 4 × 10 ft. weighs 4994 lbs., what will the contents of a tank 7 × 12 × 19 ft. weigh?

12. If it takes 2 cu. yds. of concrete to make 40 posts 6" x 4" x 7', how many yards will it take to make 678 posts 4" x 4" x 5'?

is

13. If the weight of a volume of water 1 × 11 × 9 ft. (pupil fill blank), what is the weight of a piece of ebony×× 3 ft., ebony weighing 1.33 times as much as water of equal volume?

POWERS

In the figure how many units are there on each side of

the square? How many in the whole square? There are 9 square units in a square of 3 units on a side, therefore, 9 is said to be the Square of 3. Similarly, a square with 4 units on each. side has a total of 16 square units.

The Square of a number is the product of a number with itself.

444. In the figure how many units are there on each edge? How many cubic units in the cube? There being 27 cubic units in a cube with 3 units

on an edge, 27 is said to be the Cube of 3.

The Cube of a number is the product of the number taken 3 times as a factor.

445. Squares and cubes are called Powers of a number. As the square and the cube are the second and third powers of numbers, so taking the number 4 times as a factor gives the fourth power, 5 times the fifth, etc.

446. The power of a number to be taken is indicated by a small figure written above and to the right of the