A puzzle by French puzzle maven Pierre Berloquin:
Timothy rides a bicycle on a road that has four parts of equal length.
The first fourth is level, and he pedals at 10 kph.
The second fourth is uphill, and he pedals at 5 kph.
The third fourth is downhill, and he rides at 30 kph.
The fourth fourth is level again, but he has the wind at his back, so he goes 15 kph.
What is his average speed?
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Let L be the length in kilometers of each fourth of the road. Then Timothy covers the first fourth in L/10 hours, the second fourth in L/5 hours, the third fourth in L/30 hours, and the fourth fourth in L/15 hours. The total time is L/10 + L/5 + L/30 + L/15 = 2L/5.
Since speed equals distance divided by time, we can get Timothy’s average speed by dividing the length of the whole road, 4L, by the total time:
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