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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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pure algebra | Comment 1 of 14
Let's say from A to B:
x = miles going uphill
y = miles on a level road
z = miles going downhill

Time = Distance / Rate of speed
so...

x/90 + y/72 + z/60 = 5 hours
and
x/60 + y/72 + z/90 = 4 hours

subtract the two equations together and you have:

(x/90 + z/60) - (x/60 + z/90) = 1 hour

using more algebra (is it okay if I leave this as an exercise to the reader?), we can find that

z = 180 + x

and then plugging back into one of the first equations up top:

y = 124 - 2x

Remember that we want to find the TOTAL distance between A and B, not the individual distances of x, y, and z. So we want to find:

x + y + z
= x + (124-2x) + (180+x)
= 304 miles


  Posted by Happy on 2002-05-15 09:14:35
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