Question

It takes an apprentice four times as long as the experienced plumber to replace the pipes under an old house. If it takes them 15 hours when they work together, how long would it take the apprentice alone?

Answer 1

Let's assume that the experienced plumber can complete the job in x hours.

According to the problem, the apprentice takes four times as long as the experienced plumber to complete the job. Therefore, the apprentice can complete the same job in 4x hours.

If they work together, they can complete the job in 15 hours. Therefore, we can write the following equation based on their combined work rate:

1/x + 1/4x = 1/15

Multiplying both sides by the common denominator of 60x gives:

60 + 15 = 4x

75 = 4x

x = 75/4

x = 18.75

Therefore, the experienced plumber can complete the job in 18.75 hours.

Using the relationship that the apprentice takes four times as long as the experienced plumber to complete the job, we can find the time it takes for the apprentice to complete the job alone:

4x = 4(18.75) = 75

Therefore, the apprentice would take 75 hours to complete the job alone.