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From A to B (Posted on 2002-05-15) Difficulty: 5 of 5
A car drives downhill with the speed of 90 m/h. On a level road, the same car goes 72 m/h, and uphill it goes "only" 60 m/h.

It takes this car 5 hours to go from town A to town B. The return trip only takes 4 hours.

Find the distance between the two towns.

See The Solution Submitted by levik    
Rating: 3.8667 (15 votes)

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Solution Alternate approach | Comment 6 of 14 |
I tackled the probem a little differently.

First consider that on a round trip, you can divide the road simply into flat and graded sections, without regard to whether the graded section is uphill or downhill. (Because if it is uphill on the first leg, it will be downhill on the return trip, and vice versa). let d= the distance between the towns and l= the combined length of graded sections (the combined lenth of flat sections = d-l

The speed on a flat section is 72 mph.

The average speed of a round trip on a graded section of length l is 2l (the length of the round trip) divided by the time necessary to complete the round trip (l/60 + l/90 = 3l/180 +2l/180 = 5l/180 =l/36), which works out to 2l/(1/36) = 72 mph.

The problem can be represented as 2[(d-l)/72 + l/72] =9 or after simplifying, d/72 =4 which works out to d=324. Note that l only dropped out because the average speed of a round trip on a graded stretch is the same as the speed on a flat stretch, a fact that is obvious in this approach, but not obvious in the approach everyone else used. If the speed on the flat had been given as 70 mph or 75 mph, this approach would be able to explain why the answer was not a constant

  Posted by TomM on 2002-05-16 08:29:54
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