Question 1120830: Express commuter train #12 leaves the downtown station and travels at an average speed of 55miles per hour towards the north side station, which is 16miles away. Twelve minutes later, express commuter train #7 leaves the north side station and travels at an average speed of 45miles 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?
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Train #12 travels for 12 minutes (1/5 hour) at 55mph before train #7 starts; the distance train #12 travels in that time is (1/5)(55) = 11 miles. So when train #7 starts, the trains are 16-11 = 5 miles apart.
The combined speeds of the two trains is 100mph; together to travel those 5 miles requires 5/100 = 1/20 hour, or 3 minutes.
So the trains meet when train #12 has been traveling for 12+3 = 15 minutes and train #7 has been traveling for 3 minutes.
The ratio of the speeds of the two trains is 55:45 or 11:9, so train #12 travels 11/20 of those 5 miles and train #7 travels 9/20 of the 5 miles. 11/20 of 5 miles is 2.75 miles; so when the trains meet train #12 has traveled 11+2.75=13.75 miles.
Answers: When the trains pass, train #12 is 13.75 miles from its starting point at the downtown station, and it has been traveling for 15 minutes.
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