Three Runners Puzzle

Here is another problem from Presh Talwalkar which he says is adapted from India’s Civil Services Exam.

“There are three runners X, Y, and Z. Each runs with a different uniform speed in a 1000 meters race.  If X gives Y a start of 50 meters, they will finish the race at the same time.  If X gives Z a start of 69 meters, they will finish the race at the same time.  Suppose Y and Z are in a [1000 meter] race. How much of a start should Y give to Z so they would finish the race at the same time?”

Even though Talwalkar’s original graphic showed all the runners in a 1000 meter race, it was not immediately clear to me from the wording that the race between Y and Z was also 1000 meters.  But that was the case, so I made it explicit.

See the Three Runners Puzzle

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