Question

Jeffrey can paint a house in 6 days, but if he gets a helper, he can do it in 4 days. How long would it take the helper to paint the house alone?

Answer 1

12 days

Explanation:

Jeffrey's rate is 1/6 house per day; together their rate is 1/4 house per day.

Their total rate is the sum of their individual rates, so we have ...

total rate = Jeffrey's rate + Helper's rate

1/4 house/day = 1/6 house/day + Helper's rate

(1/4 -1/6) house/day = Helper's rate = 1/12 house per day

It would take the Helper 12 days to paint the house alone.