SOLUTION: A train leaves Union Staion 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

Question 520120: A train leaves Union Staion 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.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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.
:
Let a = Train A's speed
Let b = Train B's speed
:
When they meet, the sum of their distances will equal 216 km
Write a distance equation for each Scenario
:
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
:
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
:
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
:
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
:
:
You can check these solutions in both scenario equations.
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