Problem 14 · 1994 AJHSME
Medium
Ratios, Rates & Proportions
total-divided
Two children at a time can play pairball. For 90 minutes, with only two children playing at a time, five children take turns so that each one plays the same amount of time. The number of minutes each child plays is
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Answer: E — 36.
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Hint 1 of 2
Two kids are always playing, so the game produces TWO 'player-slots' every minute — count the total slot-time first, then hand it out fairly.
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Hint 2 of 2
Total playing-time available = 2 slots × 90 minutes. Share that pot equally among the 5 children.
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Approach: total child-minutes, shared equally
- Each minute fills 2 playing spots, and the game runs 90 minutes, so there are 2 × 90 = 180 'child-minutes' of play to give out.
- Five children split it evenly: 180 ÷ 5 = 36 minutes each.
- The key move is counting total work in 'person-units' (here child-minutes) before dividing — the same trick behind 'if 3 painters take 4 hours, that's 12 painter-hours of work.' Reality check: 36 < 90, which makes sense since nobody plays the whole time.
Mark:
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