Bunuel wrote:

It takes Avery 3 hours to build a brick wall while Tom can do it in 2.5 hours. If the two start working together and after an hour Avery leaves, how much time will it take Tom to complete the wall on his own?

A. 25 minutes.

B. 30 minutes.

C. 40 minutes.

D. 55 minutes.

E. 1 hour and 20 minutes.

Despite these numbers' initial appearances, a straight combined rate approach is quick -- well under a minute.

Combined rateAvery's rate = \(\frac{1}{3}\)

Tom's rate = \(\frac{1}{2.5} = \frac{1}{\frac{5}{2}} =\frac{2}{5}\)

Add their rates:

\(\frac{1}{3} + \frac{2}{5} =\frac{(5+6)}{15} =\frac{11}{15}\)

Fraction of work done togetherWorking together at this rate for one hour, they finish \((1)(\frac{11}{15}) = \frac{11}{15}\) of the work

Work remaining for Tom aloneThe work, 1 wall, W = \(\frac{15}{15}W\)

Fraction of work left for Tom:

\((\frac{15}{15}W) - (\frac{11}{15}W) = \frac{4}{15}W\) remains

Time in minutes for Tom to finish?Time needed for Tom to finish, where

\(t = \frac{W}{r}\), and Tom's rate = \(\frac{2}{5}\)

\(\frac{\frac{4}{15}}{\frac{2}{5}}\) = \((\frac{4}{15}) * (\frac{5}{2}) =\frac{2}{3}hr\)

Multiply any fraction of an hour by 60 to find minutes.

\(\frac{2}{3}hr\) * 60 = 40 minutes

Answer C

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that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"