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Faster (Posted on 2004-11-29) Difficulty: 2 of 5
You traveled three hours at a certain speed. If you had taken 1 minute less to do each mile you would have gone 30 miles farther than you actually did.

How far did you go?

See The Solution Submitted by Charlie    
Rating: 3.4545 (11 votes)

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Solution Solution | Comment 6 of 10 |

The distance is 60 miles.

The trick is to realize that v1 + 10 mph = v2, and at what point does the interesting function "1 minute less to do each mile"  create an increase of 10 mph or 1m/6min. The only possible speed that this occurs is 20 mph which makes v2 = 30 mph.

I say this is an interesting function because it increases exponentially until 60 mph, and it decreases exponentially from  to 60. I suppose if you were doing 60mph and then started taking a minute less to do each mile, you would quickly disproove Einstien's theory of relativity!

I re-edited this comment to try to explain my line of thinking more clearly. I hadn't realized that this solution was a little bit different from the others posted.

Michael

Edited on November 30, 2004, 5:56 am
  Posted by Michael Cottle on 2004-11-30 05:44:39

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