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

_________________

Sometimes at night I would sleep open-eyed underneath a sky dripping with stars.

I was alive then.

—Albert Camus