Problem 13 · 2014 Math Kangaroo
Medium
Logic & Word Problems
caseworktotal-then-divide
In a shared apartment where six girls live there are 2 bathrooms. Each morning from 7:00 the girls use the bathrooms before breakfast, each spending 9, 11, 13, 18, 22 and 23 minutes respectively, always alone in one of the two bathrooms. What is the earliest time that all six girls can have breakfast together?
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Answer: B — 7:49
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Hint 1 of 2
Two bathrooms run in parallel; minimise the longer of the two totals.
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Hint 2 of 2
Split the six times into two groups whose sums are as close as possible.
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Approach: balance the two bathrooms (minimise the larger total)
- The six times total 9+11+13+18+22+23 = 96 minutes, shared by two bathrooms running in parallel, so we want to split them into two groups whose larger sum is as small as possible.
- A perfect 48/48 split is impossible, but 23+13+11 = 47 and 22+18+9 = 49 is the closest, so one bathroom needs 49 minutes.
- Everyone is finished after 49 minutes, i.e. at 7:49.
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