Train A and train B travel towards each other from town A and town B respectively at a constant speed.
The two towns are 1320 kilometres apart. After the two trains meet, Train A takes 5 hours to reach town B while Train B takes 7.2 hours to reach town A. How many kilometers does Train A run per hour?
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The trains have run for time t when they meet. Then the speed of A is given by
and the speed of B is given by
We also know that the distances traveled by each train in t hours add to 1320:
Putting this together we will have an equation in t:
Divide each term by 1320 (a sloppy way to say "factor 1320 from the left hand side and then divide both sides...):
Multiply both sides by the denominator of the first fraction:
Multiply both sides by the denominator of the second fraction (the only one left):
t(7.2+t)+t(5+t) = (5+t)(7.2+t)
Now let's multiply this stuff out and try to clean it into a solveable quadratic:
So `t=+-6` but we only care about the positive answer.
Now you can find the speed of train A!
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