During a recent BrainBashers race meeting, the fastest driver managed to complete a lap with an average speed of 150 mph.

They managed to complete the first two fifths of the lap at a speed of 123 mph and the second two fifths of the lap at a speed of 164 mph.

At what speed was the final one fifth of the lap length covered?

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Answer

205 mph.

Reasoning

Over the years I've had quite a few emails about this puzzle and many methods have been suggested but only the one below gives the correct answer.

If we take the number of miles in a lap to be L miles and use time = distance / speed.

The first 2/5 are covered at 123 mph. Therefore, the time taken was [(2/5) x L] / 123 hours.

The next 2/5 are covered at 164 mph. Therefore, the time taken was [(2/5) x L] / 164 hours.

The last 1/5 is covered at y mph. Therefore, the time taken was [(1/5) x L] / y hours.

The entire trip is covered at an average of 150 mph. we can conclude that:

2L 2L L L

————— + ————— + ——— = ———

5x123 5x164 5y 150

Rearranging and simplifying gives:

1 1 2 2

— = —— - ——— - ———

y 30 123 164

That means that y = 1 / (1/30 - 2/123 - 2/164)

Therefore y = 205.

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