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 From A to B (Posted on 2002-05-15)
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.

 Submitted by levik Rating: 3.8667 (15 votes) Solution: (Hide) First, label the uphill distance X, the level ground distance Y, and downhill distance Z. (This is for the first trip. On return X becomes the downhill distance and Z becomes uphill.) We are looking for the total distance, or X + Y + Z The time to travel a distance D at a particular speed V is D/V. Therefore we know that for the trip from A to B the following holds true: `1: X/60 + Y/72 + Z/90 = 5` Coming back from B to A the equation will look like this:`2: X/90 + Y/72 + Z/60 = 4` By Subtracting (2) from (1) we get:```3: X/180 - Z/180 = 1 (X - Z)/180 = 1 X - Z = 180 X = 180 + Z``` Plug this into (1) to get:```4: (180+Z)/60 + Y/72 + Z/90 = 5 3 + Z/60 + Z/90 + Y/72 = 5 5*Z/180 + Y/72 = 2 Y/72 = 2 - (5*Z/180) Y = 72*2 - 72*(5*Z)/180 Y = 144 - (20*Z)/10 Y = 144 - 2*Z``` Now that we can express both X and Y in terms of Z, plug these expressions into the formula we need to find the value of:```5: X + Y + Z = (180 + Z) + (144 - 2*Z) + Z = 324 + 2*Z - 2*Z = 324```

 Subject Author Date Puzzle Solution With Explanation K Sengupta 2007-06-12 11:43:43 Answer K Sengupta 2007-06-12 11:29:46 Not so hard David Johnson 2007-01-15 23:52:11 a philosophical remark -better late than never Ady TZIDON 2004-01-31 12:16:03 Simpler Algebra Charlie 2003-02-10 02:50:33 re(3): Alternate approach Cory Taylor 2002-11-26 09:16:35 re(2): Alternate approach levik 2002-11-25 10:39:20 re: Alternate approach Cory Taylor 2002-11-25 05:01:05 Alternate approach TomM 2002-05-16 08:29:54 I can't subtract... Happy 2002-05-16 03:48:12 re: pure algebra Ender 2002-05-16 03:09:06 re: pure algebra levik 2002-05-15 11:57:44 oops, reverse that Happy 2002-05-15 09:17:10 pure algebra Happy 2002-05-15 09:14:35

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