Question 520120
A train leaves Union Station for Central Station, 216 km away, at 9:00 am. 
One hour later a train leaves Central Station for Union Station.
 They will meet at noon.
 If the second train had started at 9:00 am, and the first train at 10:30 am, they would still have met at noon.
 Find the speed of each train.
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Let a = Train A's speed
Let b = Train B's speed
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When they meet, the sum of their distances will equal 216 km
Write a distance equation for each Scenario
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From the information given for the 1st scenario, travel times:
a = 3 hrs when they meet,  b = 2 hrs when they meet
3a + 2b = 216 km
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From the information given for the 2nd scenario, travel times:
a = 1.5 hrs when they meet,  b = 3 hrs when they meet
1.5a + 3b = 216 km
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Two equations we can solve
3a + 2b = 216
1.5a+3b = 216
multiply the 2nd equation by 2, subtract the 1st equation
3a + 6b = 432
3a + 2b = 216
---------------subtraction eliminates a, find b
4b = 216
b = 216/4
b = 54 km/h, speed of train B
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Find a
3a + 2b = 216
3a + 2(54) = 216
3a = 216 - 108
3a = 108
a = 108/3
a = 36 km/h, speed of train A 
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You can check these solutions in both scenario equations.