Problem 8 · 2020 Math Kangaroo
Easy
Ratios, Rates & Proportions
Algebra & Patterns
substitution
When Julia goes from home to school, she can walk half the way and take the bus for the other half. If she walks the whole way instead, she spends 45 minutes more. How much less time does it take her to go to school if she takes the bus the whole way?
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Answer: B — 45 minutes
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Hint 1 of 2
Let the full walk take W minutes and the full bus ride take B minutes; write the mixed trip as half of each.
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Hint 2 of 2
Compare 'walk only' with the half-and-half trip to find W − B, then compare 'bus only' with the mix.
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Approach: set up the half-and-half relation
- Mixed trip = W/2 + B/2; walking only = W. Walking is 45 min more: W − (W/2 + B/2) = 45, so (W − B)/2 = 45.
- The bus saves over the mixed trip by (W/2 + B/2) − B = (W − B)/2.
- That is the same (W − B)/2 = 45 minutes.
- So the bus-only trip takes 45 minutes less, choice B.
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