Question

Tiana can clear a football field of debris in 3 hours. Jacob can clear the same field in 2 hours. If they decide to clear the field together, how long will it take them?

50 minutes
1 hour 5 minutes
1 hour 12 minutes
5 hours

Answer 1

Given:
Tiana can clear a football field of debris in 3 hours.
Jacob can clear the same field in 2 hours.

Number of hours to complete the Job.
Tiana - 3 hours
Jacob - 2 hours
Tiana and Jacob - t

Work done per hour:
Tiana = 1/3 per hour
Jacob = 1/2 per hour
Tiana and Jacob = 1/t

Their combine work should have this equation:

1/3 + 1/2 = 1/t
(1/3*2/2) + (1/2*3/3) = 1/t
2/6 + 3/6 = 1/t
5/6 = 1/t
t(5/6) = 1
t = 1 * 6/5
t = 6/5
t = 1.20 hours

60 minutes * 0.20 = 12 minutes

1.20 hours → 1 hour and 12 minutes.

It would take 1 hour and 12 minutes if they decide to clear the field together.