SOLUTION: Two trains pass eachother in opposite directions. After 18 seconds they are 500m apart. If they travel atthe same speeds in the same direction, they are 50m apart in 15 seconds. Fi

Question 974644: Two trains pass eachother in opposite directions. After 18 seconds they are 500m apart. If they travel atthe same speeds in the same direction, they are 50m apart in 15 seconds. Find the speeds of the two trains in km per hour.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
When traveling in opposite directions, it is as if one train is standing still and the other is moving at speed v1 + v2
When traveling in the same direction, it is as if one train is standing still and the other is traveling at speed v1 - v2
Since speed x time = distance, we can write two equations in two unknowns:
18(v1+v2) = 500 -> v2 = 500/18 - v1
15(v1-v2) = 50 -> v1 = 50/15 + v2 -> v1 = 50/15 + 500/18 - v1
Solving for v1, we get v1 = 110/9 meters per second
Converting to km/hr, we get 110/9 * 3600 sec/hr / 1000 m/km = 44 km/hr
So the other train is moving at v2 = (110/9 - 50/15)*3600/1000 = 32 km/hr

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