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2007 Cyprus MO/Lyceum/Problem 3

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Problem

A cyclist drives from town A to town B with velocity 40 \frac{\mathrm{km}}{\mathrm{h}} and comes back with velocity 60 \frac{\mathrm{km}}{\mathrm{h}}. The mean velocity in \frac{\mathrm{km}}{\mathrm{h}} for the total distance is

\mathrm{(A) \ } 45\qquad \mathrm{(B) \ } 48\qquad \mathrm{(C) \ } 50\qquad \mathrm{(D) \ } 55\qquad \mathrm{(E) \ } 100

Solution

Let the distance from town A to town B, in kilometers, be d.

The time it took the cyclist to travel from A to B was \frac{d}{40} hours.

The time it took the cyclist to travel from B to A was \frac{d}{60} hours.

The cyclist's mean velocity was \frac{2d}{\frac{d}{40}+\frac{d}{60}}=\frac{2d}{\frac{100d}{2400}}= \frac{4800d}{100d}=48\frac{\mathrm{km}}{\mathrm{h}} \Longr...

See also

2007 Cyprus MO, Lyceum (Problems)
Preceded by
Problem 2
Followed by
Problem 4
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