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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 |
