2022/23 AHSMC Part 1 Problem 8

Problem 8 of 16

Evan's living room has twice as much area as Victoria's, and three times as much area as Kyle's. Kyle mops floors half as fast as Victoria and one third as fast as Evan. If they all start mopping their floor at the same time, who will finish mopping first?

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Solution

If $a$ denotes Evan's living room area, then Victoria's living room area is $\dfrac{a}{2}$ and Kyle's living room area is $\dfrac{a}{3}$ . If $v$ denotes Evan's mopping speed, then Kyle's mopping speed is $\dfrac{v}{3}$ and Victoria's mopping speed is $\dfrac{2v}{3}$ .

We conclude that Evan mops the floor in $\dfrac{a}{v}$ units of time, which is equal to Kyle's time, while Victoria mops the floor in $\dfrac{3a}{4v}$ units of time. Therefore, Victoria will be the first person who finishes mopping. The answer is (B).

University of Alberta

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