MathRevolution wrote:

Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs

B. 16hrs

C. 24hrs

D. 28hrs

E. 32hrs

* A solution will be posted in two days.

A's rate = \(\frac{1}{24}\)

B's rate is \(\frac{2}{3}\) (of) A:

\(\frac{1}{24}\) * \(\frac{2}{3}\) = \(\frac{1}{36}\) = B's rate

Amount of work for B? A works for 8 hours. \((\frac{1}{24})\) * 8 = \(\frac{1}{3}\) of the work is finished.

1 - \(\frac{1}{3}\) = \(\frac{2}{3}\) of work remains.

Time for B to finish? B has to finish remaining \(\frac{2}{3}\) of work. At B's rate, W/r = t, that will take

\(\frac{\frac{2}{3}}{\frac{1}{36}}\) =

\(\frac{2}{3}\) * 36 = 24 hours

Answer C

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"