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

You must find the relative rates of both workers...

T=f/3 and J=f/2  so if they work together to clear the field then:

ft/3+ft/2=f  make all terms have a common denominator of 6

(2/2)(ft/3)+(3/3)(ft/2)=(6/6)f

2ft/6+3ft/6=6f/6  multiply both sides by 6

2ft+3ft=6f  divide both sides by f

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

5t=6  divide both sides by 5

t=6/5 hr

t=1 1/5 hr

t=1 hr 12 min