If 5 men dig a trench 14 ft. long in 3 days, how long ought 12 men to take to dig one 28 ft. long? Put in tabular form thus:—
| Men. | Long. | Days. |
|---|---|---|
| 5 | 14 | 3 |
| 12 | 28 | ? |
First confine attention to the length of trench.
| Ft. | Ft. | Days. | Days. | |||
|---|---|---|---|---|---|---|
| 14 | : | 28 | ∷ | 3 | : | 6 |
Now we have to consider the consequences of altering the men:—
| Men. | Days. | |||||
|---|---|---|---|---|---|---|
| 5 | 6 | |||||
| 12 | ? | |||||
| Men. | Men. | Days. | Days. | |||
| 12 | : | 5 | ∷ | 6 | : | 21⁄2. |
But we could have arranged it thus and worked it out fractionally at once:—
1412 : 285 ∷ 3 : x
3 x 28 x 514 x 12 = 3⃥ × 2⃥ × 1⃥4⃥ × 51⃥4⃥ × 3⃥ × 4⃥ 2 = 52 = 21⁄2.
If practice sums are done, the meaning of each line should be marked at the end thus:—