Question 977000: Express commuter train #12 leaves the downtown station and travels at an average speed of 45miles per hour towards the north side station, which is 53.75miles away. Fifteen minutes later, express commuter train #7 leaves the north side station and travels at an average speed of 40miles 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 decimal.
12 train is ? miles from the downtown station and has been traveling for ? minutes.
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 45miles per hour towards the north side station, which is 53.75miles away.
Fifteen minutes later, express commuter train #7 leaves the north side station and travels at an average speed of 40miles 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 15 min to .25 hrs
let t = travel time of #12 train
then
(t-.25) = travel time of #7
:
Write a distance equation, dist = speed * time
When the two trains meet the sum of their travel distances = 53.7 mi
45t + 40(t-.25) = 53.7
45t + 40t - 10 = 53.75
85t = 53.7 + 10
85t = 63.7
t = 63.7/85
t = .7494 hr which is: .7494(60) = 44.96 minutes
Find the distance #12 has traveled in this time
45*.7494 = 33.7 mi
:
12 train is ? miles from the downtown station: 33.7 mi
and has been traveling for 44.96 minutes.
:
:
We cam confirm this by finding the dist #7 travels
40(.7494-.25) =
40(.5) = 20 mi, the dist of #7
20 + 33.7 = 53.7 mi
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