Average speed over three laps at different speeds

A car completes three laps of the same circuit, lapping at $100$ mph the first time, $150$ mph the second time and $200$ mph the third time. What is its average speed in mph across the three laps?

$1800/13\approx138.5$ mph. Equal distances, not equal times, so use the harmonic mean: average speed $=\dfrac{3}{\tfrac1{100}+\tfrac1{150}+\tfrac1{200}}=\dfrac{3}{13/600}=\tfrac{1800}{13}$.