SOLUTION: Express commuter train #12 leaves the downtown station and travels at an average speed of 45 miles per hour towards the north side station, which is 36 miles away. Twelve minutes l
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Question 1145370: Express commuter train #12 leaves the downtown station and travels at an average speed of 45 miles per hour towards the north side station, which is 36 miles away. Twelve minutes later, express commuter train #7 leaves the north side station and travels at an average speed of 45 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 been traveling? Answer by ikleyn(52786) (Show Source):
The rate of train #12 is 45 miles per hour.
The rate of ttrain #7 is the same 45 miles per hour.
Let " t " be the time to the passing moment, in hours, counted after train #12 starts.
Then the travel time for the train #7 is (t-0.2) hours, where 0.2 = 0.2 of an hour = 12 minutes.
Write the equation for the total distance
45*t + 45*(t-0.2) = 36.
Simplify and solve for " t ".
45t + 45t - 9 = 36
90t = 36 + 9 = 45
t = 45/90 = 0.5 of an hour = 30 minutes.
Thus train #12 traveled 0.5 of on hour, or 30 minutes, before passed train #7.
It covered the distance = 22.5 miles from the downtown station.
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