SOLUTION: Can someone help with this problem! I can't seem to figure it out and my parents are of no help. The rail line between two cities consist of two segments, one 96km longer than t

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Question 21642: Can someone help with this problem! I can't seem to figure it out and my parents are of no help.
The rail line between two cities consist of two segments, one 96km longer than the other. A passenger train averages 60km/h over the shorter segment, 120 km/h over the longer, and 100 km/h for the entire trip. How far apart are the cities?
Answer by glabow(165) About Me  (Show Source):
You can put this solution on YOUR website!
What you need to know is that the time it takes to travel over a distance is given by distance+%2F+speed+=+time.
This problem has three distances that are given as a shorter distance, a longer distance that is the short distance plus 96, and the total distance which (of course) is their sum.
Let x be the shorter distance. The time it took to travel over x was x+%2F+60. The time it took to travel over x + 96 was +%28x+%2B+96%29+%2F+120. The time it took to travel over the entire distance was +%28x+%2B+x+%2B+96%29+%2F+100.
Of course, the time for the total distance must equal the sum of the times for each segment, so
%28x+%2F+60%29+%2B+%28%28x+%2B+96%29+%2F+120%29+=+%282x+%2B+96%29+%2F+100
You solve this for x.
%282x+%2F+120%29+%2B+%28%28x%2B96%29%2F120%29+=+%282x%2B96%29%2F100 [get common denominator]
%283x%2B96%29%2F120+=+%282x%2B96%29%2F100 [simplify]
300x+%2B%28100%29%2A%2896%29=240x+%2B%28120%29%2A%2896%29 [multiply both sides by both denominators]
60x+=+%2820%29%2A%2896%29 [simplify]
3x+=+96 [divide both sides by 20]
x=32 [divide both sides by 3]
So, x+96= 128, and the total distance is 160.
Check by calculating the time taken for each segment and for the total:
32/60 = .5333333333...
128/120 = 1.06666666...
160/100 = 1.6
.5333333... + 1.06666666... = 1.6 [think of it as .5 and 1/3 of a tenth plus 1.0 and 2/3 of a tenth, which is 1.5 plus a whole tenth]