# Puzzle ZTXP

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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?

205 mph.

Reasoning

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.

Note: BrainBashers has a Dark Mode setting.