Walking, running, cycling
Weekly Problem 44 - 2006
How long does it take an athelete to walk, cycle and run three miles if this is 10 minutes slower than cycling the whole distance?
How long does it take an athelete to walk, cycle and run three miles if this is 10 minutes slower than cycling the whole distance?
Age
11 to 14
Challenge level
Problem
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 which challenges you to use similar mathematical ideas.
Student Solutions
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.