At the local racetrack, Alex was testing the latest car.

During the eight test laps, Alex managed to average the first two laps at 100mph, the next two laps at 102mph, the next two laps at 140mph, and the last two laps at 150mph.

What was the average speed for the entire 8 laps?

Puzzle Copyright © Kevin Stone

workings
hint
answer
print

Share link – www.brainbashers.com/puzzle/zbip

Hint

Remember that Time = Distance ÷ Speed, and try setting the track length to be a random length.

Answer

119mph.

Reasoning

It doesn't matter how long a lap is, so let's set the track length to be a random number, say 5 miles.

Using:

Time = Distance ÷ Speed

The first two laps took:

^{10}/_{100} hours

The second two laps took:

^{10}/_{102} hours

The next two laps took:

^{10}/_{140} hours

The final two laps took:

^{10}/_{150} hours

Therefore, the total time for the 8 laps was:

^{10}/_{100} + ^{10}/_{102} + ^{10}/_{140} + ^{10}/_{150} hours

The 8 laps were 40 miles, and using Speed = Distance ÷ Time:

average speed = 40 ÷ (^{10}/_{100} + ^{10}/_{102} + ^{10}/_{140} + ^{10}/_{150})

= 119 mph

**Note:** BrainBashers has a Dark Mode option – I recommend **not** using your browser's dark mode or extensions for BrainBashers