Problem 15 · 2017 Math Kangaroo
Medium
Logic & Word Problems
caseworktotal-then-divide
David has a stove with two hobs on which he wants to prepare five different dishes. The dishes need 40 min, 15 min, 35 min, 10 min and 45 min until they are fully cooked. He wants to spend as little time in the kitchen as possible but is only allowed to take dishes off the hob when they are fully cooked. How long does he need for the preparation?
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Answer: C — 75 min
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Hint 1 of 2
With two hobs, split the five cooking times into two groups; the time needed is the larger group's total.
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Hint 2 of 2
Balance the two groups as evenly as you can to make that larger total small.
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Approach: partition the times into two groups and minimise the larger total
- The five times add to 40+15+35+10+45 = 145 minutes across two hobs.
- He is free until everything is cooked, so the time needed is the larger group's total.
- The most balanced split is 40+35 = 75 against 45+15+10 = 70.
- The larger total, and so the time needed, is 75 min.
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