Bunuel wrote:

Sam can complete a certain task in 4 hours while Peter needs only 3 hours to complete the same task. If Sam starts working on the task and half an hour later Peter joins him, how many hours will it take them to complete the task together?

A. 3/2

B. 12/7

C. 2

D. 31/14

E. 5/2

Rates:

Sam's rate: \(\frac{1}{4}\)

Peter's rate: \(\frac{1}{3}\)

Combined rate: \(\frac{1}{4} +

\frac{1}{3}=\frac{7}{12}\)

First part of work:

Sam alone for \(\frac{1}{2}\) hour. R*T = W

\(\frac{1}{4} * \frac{1}{2} =\frac{1}{8}\) W finished

\(\frac{7}{8}\) of work remains for both to finish

Second part of work, W/R = T

\(\frac{\frac{7}{8}}{\frac{7}{12}} =(\frac{7}{8} * \frac{12}{7}) = \frac{12}{8}=\frac{3}{2}\)

Answer A

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"