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To Run or Not to Run?

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

An athlete covers three consecutive miles by walking the first mile, running the second mile and cycling the third. He runs twice as fast as he walks, and he cycles one and a half times as fast as he runs. He takes ten minutes longer than he would do if he cycled the three miles. How long does he take by walking, running and cycling?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.


This problem is taken from the UKMT Mathematical Challenges.
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