SOLUTION: Express commuter train #12 leaves the downtown station and travels at an average speed of 5050miles per hour towards the north side station, which is 3737miles away. Twelve minutes

Question 1092564: Express commuter train #12 leaves the downtown station and travels at an average speed of 5050miles per hour towards the north side station, which is 3737miles away. Twelve minutes later, express commuter train #7 leaves the north side station and travels at an average speed of 4040miles 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.
#12 train is.... miles from the downtown station and has been traveling for
.... minutes.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

12 minutes is 1/5 of an hour, so the distance train #12 has traveled when train #7 starts is 1/5 of 5050 miles, or 1010 miles. So when train #7 starts, the distance between the two trains is 3737-1010 = 2727 miles.

When the two trains are traveling towards each other, the rate at which the distance between them is changing is the sum of the speeds of the two trains, which is 5050+4040 = 9090 mph.

The amount of time for the two trains together to travel 2727 miles at a combined speed of 9090 mph is 2727/9090 = 0.3 hours, or 18 minutes.

So when the two trains pass each other, train #12 has been traveling a total of 12+18 = 30 minutes, or half an hour.

So when the two trains pass each other, the distance train #12 is from where it started is 0.5*5050 = 2525 miles.
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