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Puzzle Details

During a recent Formula 1 race meeting, Sterling managed to complete a lap with an average speed of 150 mph. He managed to complete the first two fifths of the lap length at a speed of 123 mph and the second two fifths of the lap length at a speed of 164 mph. At what speed was the final one fifth of the lap length covered - the answer is not 176 mph?

[Ref: ZTXP] © Kevin Stone

we have had a lot of queries on 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 x miles and using time = distance / speed.
The first 2/5 are covered at 123 mph. Therefore, the time taken was [(2/5) * x] / 123 hours.
The next 2/5 are covered at 164 mph. Therefore, the time taken was [(2/5) * x] / 164 hours.
The last 1/5 is covered at y mph. Therefore, the time taken was [(1/5) * x] / y hours.
The entire trip is covered at an average of 150 mph. we can conclude that:

2x      2x      x      x
----- + ----- + --- =  ---
5*123   5*164   5*y    150

Working this out we get:

1     -2    -2    1
-- - --- - --- =  -
30   123   164    y

The means that y = 1 / (1/30 - 2/123 - 2/164)
Therefore y = 205.

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