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 9 hours when they work together, how long would it take the apprentice alone?

Answer 1

The experienced plumber takes 9 hours, and it takes the apprentice 4 times as long to complete the job. So, it would take the apprentice 36 hours to complete the job alone.

Step-by-step explanation:

Let's say that the experienced plumber takes x hours to replace the pipes under the old house. According to the question, it takes the apprentice four times as long, so the apprentice would take 4x hours to complete the job alone.

When they work together, they complete the job in 9 hours. So we can create the equation:

1/x + 1/(4x) = 1/9

To solve this equation, we can multiply both sides by 36x to get:

36 + 9 = 4x + x

45 = 5x

x = 9

Therefore, it takes the experienced plumber 9 hours and the apprentice would take 4 times that, which is 36 hours, to complete the job alone.

Answer 2

It takes an apprentice four times as long as the experienced plumber to replace the pipes under an old house. It takes them 14 hours when they work together.

Step-by-step explanation:

5/(4x) = 1/14

x = 35/2

The plumber takes x = 35/2 hours to replace the pipes alone.

The apprentice takes 4x = 70 hours to replace the pipes alone.