Question

Pat has been assigned the job of picking apples from the family orchard. He could do the job alone in 8 hours. He knows that his sister, Patti, could do the job in 7 hours. He begs her to help, and she agrees. How long will both of them take to pick the apples? (Round your answer to the nearest tenth.)

Answer 1

3.7 hours

Explanation:

Pat could do the job alone in 8 hours.

Patti could do the job alone in 7 hours

Output = Rate * time

Let the rate at which pat does the work = Rp

Let the rate at which Patti does the work = Rt

Let X be the total output

Rp * 8 = X

Rp = X/8

Rt * 7 = X

Rt = X/7

If both pat and Patti pick apples, we have

(Rp+Rt)T = X

(X/8 + X/7)T = X

[(7X + 8X)/56]T = X

[X(7+8)/56]T = X

Divide both sides by X

[(7+8)/56]T = 1

(15/56)T = 1

T = 56/15

T = 3.7 hours