A train overtakes two people walking beside the track in its direction of travel. It passes one, walking at 3 km/h, in 20 seconds and the other, walking at 6 km/h, in 21 seconds. What is the speed of the train?

Explanation

1. 01

   Let the speed be $v$ km/h. The train's length is the same both times.

2. 02

   $(v - 3) \times 20 = (v - 6) \times 21$ (the unit conversion cancels on both sides).

3. 03

   $20v - 60 = 21v - 126$, so $v = 66$ km/h.

4. 04

   Check: 63 km/$h = 17.5$ m/s, and $17.5 \times 20 = 350$ m; 60 km/$h \times 21$ s also gives 350 m.