Question

Two plumbers received a job. At first, one of the plumbers worked alone for 1 hour, and then they worked together for the next 4 hours. After this 40% of the job was complete. How long would it take each plumber to do the whole job by himself if it is known that the first plumber would take 5 more hours to finish the job than the second plumber?

Answer 1

To find how long each plumber would take to do the whole job by themselves, we can set up an equation using their work rates. By solving this equation, we can determine the time it would take for each plumber to complete the job individually.

Step-by-step explanation:

To solve this problem, let's consider the work rate of each plumber. Let's assume that the second plumber can complete the whole job in x hours. Since the first plumber would take 5 more hours to finish the job than the second plumber, the first plumber would take (x+5) hours to complete the job.

Now, let's calculate the combined work rate of both plumbers when they work together. We know that after working together for 4 hours, 40% of the job was completed. This means that the work done by both plumbers in 4 hours is equal to 40% of the total job.

Using the work rate formula, the combined work rate of both plumbers is 40% of the job done in 4 hours. This can be expressed mathematically as:

work rate of first plumber + work rate of second plumber = 40% of the job done in 4 hours

(1 / (x+5)) + (1 / x) = 0.4

Solving this equation will give us the value of x, which represents the number of hours the second plumber would take to complete the job alone. The first plumber would take (x+5) hours to complete the job.