SOLUTION: It takes 12 seconds for two trains to pass one another when moving in opposite directions. If they are in the same direction, it will take the faster train 3 minutes to pass the sl

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Question 346023: It takes 12 seconds for two trains to pass one another when moving in opposite directions. If they are in the same direction, it will take the faster train 3 minutes to pass the slower one. If the trains are 130 meters and 120 meters long, respectively, what are the rates of the two trains?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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It takes 12 seconds for two trains to pass one another when moving in opposite directions.
If they are in the same direction, it will take the faster train 3 minutes to pass the slower one.
If the trains are 130 meters and 120 meters long, respectively, what are the rates of the two trains?
:
Let a = speed of the faster train
let b = speed of the slower
:
Trains meeting each other
The sum of the speed of the two trains (in meters/sec)
speed = dist/time
a + b = %28%28130%2B120%29%29%2F12
a + b = 20.83 m/sec is the sum of their speeds
:
Trains going in the same direction (change 3 min to 180 sec
a - b = %28%28130%2B120%29%29%2F180
a - b = 1.39 m/sec is the difference of their speed
:
Use elimination
a + b = 20.83
a - b = 1.39
----------------adding eliminates b, find a
2a = 22.22
a = 22.22%2F2
a = 11.11 m/sec is the speed of train a
In km/hr: %28%2811.11%2A3600%29%29%2F1000 ~ 40 km/hr
:
then using the sum equation find b
11.11 + b = 20.83
b = 20.83 - 11.11
b = 9.72 m/sec is the speed of train b
In km/hr %28%289.72%2A3600%29%29%2F1000 ~ 35 km/hr