Question 774933: 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 `30 meters and 120 meters long, respectively, what are the rates of the two trains?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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 `30 meters and 120 meters long, respectively, what are the rates of the two trains?
:
Convert 3 min to 180 seconds
:
let a = rate of train 1, (faster)
let b = rate of train 2
:
towards each other
12a + 12b = 30 + 120
12a + 12b = 150 m
:
a passing b
180a - 180b = 150
Multiply the 1st equation by 15, add to the above equation
180a + 180b = 2250
180a - 180b = 150
---------------------Addition eliminates b, find a
360a = 2400
a = 2400/360
a = 6 m/sec is the speed of the 1st train, about 24 km/hr
:
Find b
12(6.667) + 12b = 150
12b = 150 - 80
12b = 70
b = 70/12
b = 5 m/sec is the speed of the 2nd train, about 21 km/hr
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