Question 1027680: Fred and Frank are two fitness fanatics on a run from point A to B. Fred runs half the way and walks the other half. Frank runs for half the time and walks for the other half. They both run and walk at the same speeds. Who finishes first?
Answer by FrankM(1040)   (Show Source):
You can put this solution on YOUR website! As asked, the question poses two numbers, a slow and fast speed. We can do the math with all letters, variables, but no need, replacing with numbers can illustrate the issue far simpler.
I happen to run at 6mph, and walk at 4mph. Say the race is 12 miles.
Fred runs 6 miles which happens to take 1 hour, then walks 6 miles which at 4mph takes 1.5 hours. His total time is 2.5 hours.
Now, for frank, his time is X hours. At 4mph, his distance is (1/2)Xhr*4m/hr = 2X miles , At 6mph, his distance is (1/2)Xhr*6m/hr = 3X miles, total 5X=12 or X = 2.4 hours. Frank finishes first.
You can change the numbers, and find the results, the ratio of times, exactly the same.
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