Question

Robin can mow a lawn in 3 hours, while Brady can mow the same lawn in 4 hours. How many hours would it take for them to mow the lawn together?

seven twelfths

twelve sevenths

7

12

Answer 1

The answer is twelve sevenths (12/7)

x - the job
t - time to do the job x

Robin can mow a lawn in 3 hours: x/3 * t
Brady can mow the same lawn in 4 hours: x/4 * t

If they work together, the total work will be the sum of their speeds:
x = x/3 * t + x/4 * t = (x/3 + x/4)*t = (4x/12 + 3x/12) * t = 7x/12 * t

x = 7x/12 * t

Divide both sides by x:
x/x = 7x/12 * t/x
1 = 7/12 t
t = 1 : 7/12
t = 12/7