2017/18 AHSMC Part 1 Problem 6

Problem 6 of 16

Ben and Cleo can paint a fence in four days. Anna and Ben can do it in two days, Anna and Cleo in three days. How many days, as a fraction, does it take all of them working if Cleo gets injured at the end of the first day and can't come back to work?

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Solution

If $a$ is the portion of the work done per day by Anna, $b$ by Ben and $c$ by Cleo, then $b + c = \dfrac{1}{4}$ , $a + b = \dfrac{1}{2}$ , $a + c = \dfrac{1}{3}$ , hence $a + b + c = \dfrac{13}{24}$ . Thus $\dfrac{11}{24}$ of the work has to be completed by Anna and Ben. They need for this $\dfrac{11}{24} \div \dfrac{1}{2} = \dfrac{11}{12}$ days for a total of $\dfrac{23}{12}$ days. The answer is (C).

University of Alberta

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