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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: 3.4000 (10 votes)

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Solution Puzzle Solution Comment 10 of 10 |

Let the total time taken by the trveller to traverse one mile be p
minutes. Hence, in three hours the traveller would traverse 180/p miles.

If the trveller took (p-1) minutes to traverse one mile, then he
would traverse 180/(p-1) miles in three hours.

Accordingly, by conditions of the problem, we must have:

180/(p-1) - 180/p = 30
Or, 180/(p(p-1)) = 30
Or, p(p-1) = 6
Or, p^2-p-6 = 0
Or, (p+2)(p-3) = 0
Or, p=3, ignoring the negative value of p which is inadmissible.

Consequently, the required distance traversed by the traveller
in 3 hours is 180/3 = 60 miles.

Edited on April 29, 2008, 3:59 pm
  Posted by K Sengupta on 2007-10-20 00:21:15

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