Problem 8 · 1997 AJHSME
Medium
Arithmetic & Operations
total-minus-parts
Walter catches the school bus at 7:30 a.m., has 6 classes that last 50 minutes each, has 30 minutes for lunch, and has 2 hours of additional time at school. He takes the bus home and arrives at 4:00 p.m. How many minutes has he spent on the bus?
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Answer: B — 60 minutes.
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Hint 1 of 2
You can't time the bus rides directly — but you DO know the whole day and everything that wasn't the bus. The bus is whatever's left over.
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Hint 2 of 2
Indirect (complementary) counting: when one piece is hard to measure, find the whole and subtract all the easy pieces.
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Approach: whole day minus everything that isn't the bus
- The full stretch from 7:30 a.m. to 4:00 p.m. is 8½ hours = 510 minutes — this includes the two bus rides plus all of school.
- Add up everything that ISN'T the bus: 6 classes × 50 + 30 lunch + 2 hr extra = 300 + 30 + 120 = 450 minutes.
- Whatever's left must be the bus: 510 − 450 = 60 minutes (the round trip).
- You'll see it again: 'time/space spent doing X' is often easiest as total − (everything else), instead of measuring X head-on.
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