Question 573048: If it takes twice as long for a passenger train to pass a freight train after it first overtakes it as it takes for the two trains to pass when going in opposite directions, determine how many times faster the passenger train is than the freight train.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! If it takes twice as long for a passenger train to pass a freight train after it first overtakes it,
as it takes for the two trains to pass when going in opposite directions,
determine how many times faster the passenger train is than the freight train.
:
Let p = pass train speed
let f = freight speed
then
(p-f) = relative speed going the same direction
and
(p+f) = relative speed going towards each other
:
Let t = time required to pass when going towards each other
then
2t = time required for the pass train to pass the freight going the same direction
:
Combined length of the two trains is the same for each scenario
:
write a distance equation, dist = speed * time
:
2t(p-f) = t(p+f)
:
2tp - 2tf = tp + tf
combine like terms
2tp - tp = tf + 2tf
:
tp = 3tf
divide both sides by t
p = 3f
Passenger train speed is 3 times freight train speed
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