Question

Jamie can shovel the driveway in 7 hours, but if his sister Emma helps, it would take 2 hours. How long would it take Emma to shovel the driveway alone?

A. 3.5 hours
B. 4 hours
C. 5 hours
D. 6 hours

Answer 1

It would take Emma approximately 2 hours and 20 minutes to shovel the driveway alone.

Step-by-step explanation:

Let's assume that Emma takes x hours to shovel the driveway alone.

Working together, Jamie and Emma can complete the job in 2 hours. This means that in one hour, they can complete 1/2 of the job. So, the combined work done by Jamie and Emma in one hour is 1/x + 1/7.

Working alone, Jamie takes 7 hours to complete the job. This means that in one hour, Jamie can complete 1/7 of the job. So, the work done by Jamie in one hour is 1/7.

Equating the two expressions for the combined work done in one hour, we get:

1/x + 1/7 = 1/2

Multiplying through by the common denominator 2x:

2 + x/7 = x

Multiplying through by 7:

14 + x = 7x

6x = 14

x = 14/6 = 7/3 = 2 1/3.

Therefore, it would take Emma approximately 2 hours and 20 minutes to shovel the driveway alone.