Problem 25 · 2014 Math Kangaroo
Stretch
Ratios, Rates & Proportions
distance-speed-timeratio
David cycles from Edinburgh to his aunty, who lives outside Edinburgh. He wants to arrive at exactly 15:00. After 23 of his planned travel time he had covered 34 of the way. He then cycled more slowly and arrived exactly on time. In what ratio are the average speeds of the two sections of his journey?
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Answer: C — 3 : 2
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Hint 1 of 2
Take the planned time as 1 and the distance as 1; the first part used 2/3 of the time for 3/4 of the distance.
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Hint 2 of 2
Speed = distance ÷ time for each part, then compare the two speeds.
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Approach: compute each part's speed as distance over time
- Let total time = 1 and total distance = 1. First part: distance 3/4 in time 2/3, so speed = (3/4)/(2/3) = 9/8.
- Second part: the remaining 1/4 of distance in the remaining 1/3 of time, so speed = (1/4)/(1/3) = 3/4.
- Ratio of speeds = (9/8) : (3/4) = 9 : 6 = 3 : 2.
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