243. Suppose the following question asked: How long will it take 15 men to do that which 45 men can finish in 10 days? It is evident that one man would take 45 × 10, or 450 days, to do the same thing, and that 15 men would do it in one-fifteenth part of the time which it employs one man, that is, in (450 ÷ 15) or 30 days. By this and similar reasoning the following questions can be solved.
EXERCISES.
If 15 oxen eat an acre of grass in 12 days, how long will it take 26 oxen to eat 14 acres?
Answer, (96¹²/₁₃) days.
If 22 masons build a wall 5 feet high in 6 days, how long will it take 43 masons to build 10 feet?
Answer, (6⁶/₄₃) days.
244. The questions in the preceding article form part of a more general class of questions, whose solution is called the Double Rule of Three, but which might, with more correctness, be called the Rule of Five, since five quantities are given, and a sixth is to be found. The following is an example: If 5 men can make 30 yards of cloth in 3 days, how long will it take 4 men to make 68 yards? The first thing to be done is to find out, from the first part of the question, the time it will take one man to make one yard. Now, since one man, in 3 days, will do the fifth part of what 5 men can do, he will in 3 days make ³⁰/₅, or 6 yards. He will, therefore, make one yard in ³/₆6 or (3 × 5)/30 of a day. From this we are to find how long it will take 4 men to make 68 yards. Since one man makes a yard in
| 3 × 5 | of a day, he will make 68 yards in | 3 × 5 | × 68 days, |
| 30 | 30 |
| or (116) in | 3 × 5 × 68 | days; and 4 men will do this in one-fourth; |
| 30 |
| of the time, that is (123), in | 3 × 5 × 68 | days, or in 8½ days. |
| 30 × 4 |