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To Run or Not to Run?

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

Let the athlete take x minutes to cycle one mile.

Therefore he takes 3x/2 minutes to run one mile and 3x minutes to walk one mile.

Therefore 3x +3x/2 +x = 3x + 10 i.e. x = 4 The cyclist takes 12 minutes to walk the first mile, 6 minutes to run the second mile and 4 minutes to cycle the third mile, a total time of 22 minutes.

This problem is taken from the UKMT Mathematical Challenges.