Problem 26 · 2012 Math Kangaroo
Stretch
Ratios, Rates & Proportions
distance-speed-time
It takes 8 seconds for train G to pass by a milestone. Shortly afterwards the train meets train H. It takes 9 seconds for the trains to pass each other. Train H then takes 12 seconds to pass by the milestone. What can be deduced about the length of the trains?
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Answer: A — G is twice as long as H.
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Hint 1 of 2
Passing a milestone takes (own length)/(own speed); passing each other uses the combined length and speeds.
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Hint 2 of 2
Write the three timings and combine them to compare the lengths.
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Approach: translate each timing into length = speed × time and combine
- Let G have length Lg, speed vg, so Lg = 8·vg; H has Lh = 12·vh.
- The trains pass each other in 9 s: Lg + Lh = 9(vg + vh), i.e. 8vg + 12vh = 9vg + 9vh, giving vg = 3vh.
- Then Lg = 8vg = 24vh and Lh = 12vh, so Lg = 2·Lh: train G is twice as long as H (A).
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