Question

Jack and Jill are brother and sister. Jack rakes the yard in 5 hours and Jill rakes the yeard in 8 hours. Mom says to rake the yard together how long will that take? ( answer as a mixed fraction)

Answer 1

Given that Jack rakes the yard in 5 hours and Jill rakes the yeard in 8 hours. Let the amount of time that it takes them to rake the yard together be t, then:

$\frac{1}{t} = \frac{1}{5} + \frac{1}{8} \\ \\ = \frac{8+5}{40} = \frac{13}{40} \\ \\ \therefore t= \frac{40}{13} =3 \frac{1}{13}\ hours$