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?

Answer 1

Tiana can clear 1/3 of a football field in 1 hour and Jacob can clear 1/2 of a football field in 1 hour. Adding these together, they can clear 5/6 a field in 1 hour. Therefore they can clear a football in 6/5 of an hour or an hour and 12 minutes.

Answer 2

You need to use the respective rates of t and j.

t/3+t/2=1 making each term have a common denominator of 6

2t/6+3t/6=6/6 multiplying both sides by 6

2t+3t=6 combine like terms on left side

5t=6 divide both sides by 5

t=6/5

t=1.2 hours

So it would take them working together 1.2 hours to clear the field. (1 hour 12 minutes)