Question

Two workers, a trainer and trainee, working together can do a job in 3 hours. The trainer is 3 times faster than the trainee to complete the same job. How long will it take to trainee to finish the same job?

Answer 1

12 hours

Explanation:

Let's say that the trainee can do the job in $x$ hours.

Since the trainer is three times faster than the trainee, the trainer can do the same job in $x/3$ hours.

Working together, the trainer and trainee can complete the job in 3 hours, so we can set up the equation:

$$\frac{1}{x}+\frac{1}{x/3}= \frac{1}{3}$$

To solve for $x$, we can first simplify the left-hand side:

$$\frac{1}{x}+\frac{3}{x}= \frac{1}{3}$$

Combining like terms, we get:

$$\frac{4}{x}= \frac{1}{3}$$

Multiplying both sides by $x$, we get:

$$x=\frac{4}{1/3}=12$$

Therefore, the trainee can complete the job in 12 hours.