During a recent Formula 1 race meeting, Blake managed to complete a lap with an average speed of 150 mph.

They 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?

I 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.