Question 838556: Express commuter train #12 leaves the downtown station and travels at an average speed of 50 miles per hour towards the north side station, which is 35 miles away. Fifteen minutes later, express commuter train #7 leaves the north side station and travels at an average speed of 40 miles per hour towards the downtown station.
At the moment when the two trains pass each other, how far (in miles) is the #12 train from the downtown station and how long (in minutes) has the #12 train have been traveling?
If the answer is not an integer, enter it as an exact decimal.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Express commuter train #12 leaves the downtown station and travels at an average speed of 50 miles per hour towards the north side station, which is 35 miles away.
Fifteen minutes later, express commuter train #7 leaves the north side station and travels at an average speed of 40 miles per hour towards the downtown station.
At the moment when the two trains pass each other, how far (in miles) is the #12 train from the downtown station and how long (in minutes) has the #12 train have been traveling?
:
Let t = travel time of #12 when they meet
then
(t-.25) = travel time of #7 (15 min = .25 hrs)
:
When the two trains meet they will have traveled a total of 35 mi
Write a distance equation; dist = speed * time
50t + 40(t-.25) = 35
50t + 40t - 10 = 35
90t = 35 + 10
90t = 45
t = 45/90
t = .5 hrs is the travel time of #12 when they meet
then
.5(50) = 25 mi is the distance #12 is from the downtown station
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