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THE NEW  STUDENT'S  REFERENCE  WORK                                    2205

A ship sailed 47f miles in 5 hours. How long will she be in sailing 190 miles!

Let X represent the number of hours she will be in sailing 180 miles. For convenience make X (hours) the fourth term of the proportion.

Write the ratio 5 : X* 5 must be the third term of the proportion,   because   the   third   and   fourth terms form a ratio and must be of the same denominator.

We know that the ship will be longer in sailing 180 mi. than she was in sailing 47| mi. This shows that X, the consequent of the second ratio, will be greater than its antecedent, therefore to have an equality of ratios we must make the consequent of the first ratio larger than its antecedent. If, however, we find that X, the consequent of the second ratio, is to be less than its antecedent, we must make the consequent of the first ratio less than its antecedent, that the equality of the ratios may be preserved. In performing examples in proportion, remember that the terms of a ratio must be of the same denomination. Write the second ratio, making X, the number sought, the fourth term. Always ask if the consequent of the second ratio is to be larger or smaller than its antecedent, and from the answer determine the first ratio.

EXERCISE 41.

1.   James purchased 15 acres of land for $72. How much did William have to pay for 37f acres at the same rate?

2.   If 7 men eat 10| loaves of bread in a week, how many loaves will 25 men eat at the same rate in the same time ?

3.   A house was painted by  8  men in  6  days. How many men would be required to do the same work in 12 days!

4.   If a man can perform a journey in 6 days, traveling 14 hours a day, how many days will be required if he travels only 7 hours a day ?

5.   Six horses consume a certain quantity of oats in 12 days. How long will the same quantity feed 36 horses f

POWERS AND ROOTS.

A power is the product of like factors.

The product of two like factors is the 2nd power, or square of that number.

9 is the square of 3 (3X 3=9). 16 is the square of 4 (4 X 4 = 16). 25 is the square of 5 (5 X 5 = 25).

miles       miles         hours    hours

47J  190 = 5   X

sxit* = 20 **i

47| : 190 = 5 : 20