Problem 11 · 2014 Math Kangaroo
Hard
Ratios, Rates & Proportions
unit-rate
Max has a one-hour piano lesson twice a week; Hanna has a one-hour lesson only every second week. The piano lessons run over a certain number of weeks. How many weeks is this, if during this time Max has 15 more hours of lessons than Hanna?
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Answer: E — 10 weeks
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Hint 1 of 2
Work out how many extra hours Max gets over Hanna in a single week.
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Hint 2 of 2
Divide the 15-hour gap by the weekly gap to get the number of weeks.
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Approach: find the weekly difference, then divide
- Max has 2 hours each week; Hanna has 1 hour every two weeks, i.e. 0.5 hours per week on average.
- So Max gains 2 − 0.5 = 1.5 extra hours every week.
- To build a 15-hour lead takes 15 ÷ 1.5 = 10 weeks.
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