If a train takes $1.5$ seconds to cross a telegraph post and $1.75$ seconds to overtake a cyclist racing along a road parallel to the track at $10$ m/s, then the length of the train is

Let the length of the train be L meters, so its speed is L divided by 1.5 meters per second. Using the relative speed formula for overtaking the cyclist, the equation becomes L equals the relative speed multiplied by 1.75 seconds, or L equals the train's speed minus 10 multiplied by 1.75. Substituting the train's speed gives L equals L divided by 1.5 minus 10, all multiplied by 1.75, and solving this equation yields a train length of 105 meters.

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