SOLUTION: Express commuter train #12 leaves the downtown station and travels at an average speed of 50miles per hour towards the north side station, which is 56.75miles away. Twelve minutes

Question 1065736: Express commuter train #12 leaves the downtown station and travels at an average speed of 50miles per hour towards the north side station, which is 56.75miles away. Twelve minutes later, express commuter train #7 leaves the north side station and travels at an average speed of 35
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?
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 50miles per hour towards the north side station, which is 56.75miles away.
Twelve minutes later, express commuter train #7 leaves the north side station and travels at an average speed of 35 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?
:
Change 12 min to .2 hrs
let t = travel time of #7 train when they meet
then
(t+.2) = travel time of #12 which left 12 min earlier
:
Write distance equation dist = speed * time
#12 dist + #7 dist = 56.75 mi
50(t+.2) + 35t = 56.75
50t + 10 + 35t = 56.75
85t = 56.75 - 10
t = 46.75/85
t = .55 hrs is the travel time of #7
then
.55 + .2 = .75 hrs is the travel time of #12 when the two trains met
Find the distance #12 traveled in .75 hr
50 * .75 = 37.5 mi
"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?"
Train # 12 traveled 37.5 mi in 45 min to the meeting point
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