Question

If Ben can paint the house for 15 hours, and only 6 hours if Ben is working together with Jen, how many hours can Jen do the job alone?

A. 10 hours
B. 12 hours
C. 18 hours
D. 21 hours

Answer 1

Jen can paint the house alone in 18 hours. We find this by calculating rates of work and solving the equation for Jen's rate, resulting in 18 hours.

Step-by-step explanation:

The correct answer is option C. 18 hours. To solve this problem, we use the concept of rates of work. If Ben can paint the house in 15 hours, his rate of work is 1/15 of the house per hour. When Ben and Jen work together, they can finish in 6 hours, so their combined rate is 1/6.

We can find Jen's painting rate per hour by subtracting Ben's painting rate from their combined painting rate. Since Ben can paint the house in 15 hours, his painting rate is 1/15 of the house per hour. When Ben and Jen work together, they can paint the house in 6 hours, so their combined painting rate is 1/6 of the house per hour. Subtracting Ben's painting rate from the combined rate gives us Jen's painting rate, which is 1/6 - 1/15 = 1/10 of the house per hour.

We need to find Jen's rate. Let Jen's rate be 1/j where j is the number of hours it takes Jen to paint the house alone. The combined rate is then 1/15 + 1/j = 1/6. Solving for j gives us j = 1/(1/6 - 1/15), which simplifies to j = 18. Therefore, Jen can paint the house alone in 18 hours.