Again, suppose the question to be: If 5 men can make 30 yards in 3 days, how much can 6 men do in 12 days? Here we must first find the quantity one man can do in one day, which appears, on reasoning similar to that in the last example, to be 30/(3 × 5) yards. Hence, 6 men, in one day, will make
| 6 × 30 | yards, and in 12 days will make | 12 × 6 × 30 | or 144 yards. |
| 5 × 3 | 5 × 3 |
From these examples the following rule may be drawn. Write the given quantities in two lines, keeping quantities of the same sort under one another, and those which are connected with each other, in the same line. In the two examples above given, the quantities must be written thus:
SECOND EXAMPLE.
Draw a curve through the middle of each line, and the extremities of the other. There will be three quantities on one curve and two on the other. Divide the product of the three by the product of the two, and the quotient is the answer to the question.
If necessary, the quantities in each line must be reduced to more simple denominations (219), as was done in the common Rule of Three (238).
EXERCISES.
If 6 horses can, in 2 days, plough 17 acres, how many acres will 93 horses plough in 4½ days?