SOLUTION: Hi! I'm helping my stepdaughter with this problem, and we are not sure how to "set up" this problem in an equation. It is stated: A freight train leaves a station traveling 60

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Question 682308: Hi! I'm helping my stepdaughter with this problem, and we are not sure how to "set up" this problem in an equation. It is stated:
A freight train leaves a station traveling 60 miles per hour. Thirty minutes later a passenger train leaves the station in the same direction on a parallel track at a speed of 72 miles per hour. How long will it take the passenger train to catch the freight train?
Thank you!
Found 2 solutions by josmiceli, Alan3354:
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
First, you need to know how much of
a head start the freight train got

mi
----------------
Now start a stopwatch when the passenger
train leaves the station. Both trains will now
travel for the same amount of time
until they meet.
Let = the distance that the passenger
train travels until they meet
----------------
freight train's equation:
(1)
passenger train's equation:
(2)
--------------
Substitute (2) into (1)
(1)
(1)
(1)
The passenger train takes 2.5 hrs to catch the freight train
check answer:
(2)
(2)
and
(1)
(1)
(1)
OK
Note that the freight train covers mi
in the same 2.5 hrs that the passenger train goes mi

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
A freight train leaves a station traveling 60 miles per hour. Thirty minutes later a passenger train leaves the station in the same direction on a parallel track at a speed of 72 miles per hour. How long will it take the passenger train to catch the freight train?
-----------------
In 30 mins (1/2 hr) the 1st train has gone 30 miles (60*1/2)
The 2nd train gains on the 1st at 12 mi/hr (72-60)
30 mi/12 mi/hr = 2.5 hours.