Question 952608: Can you please help me with this word problem: A train leaves New York for Boston, 200 miles away, at 5:00 P.M. and averages 40 mph. Another train leaves Boston for New York on an adjacent set of tracks at 3:00 P.M. and averages 45 mph. At what time will the trains meet? (Round to the nearest minute.)
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A train leaves New York for Boston, 200 miles away, at 5:00 P.M. and averages 40 mph.
Another train leaves Boston for New York on an adjacent set of tracks at 3:00 P.M. and averages 45 mph.
At what time will the trains meet?
:
Find how many hrs from 3Pm until the meet
:
let t = travel time of the Bos/NY train (leaves at 3:00)
then
(t-2) = travel time of the NY/Bos train (leaves at 5:00)
:
We know when they will meet the sum of their distances = 200 mi
write a distance equation using this fact; dist = speed * time
40(t-2) + 45t = 200 mi
40t - 80 + 45t = 200
40t + 45t = 200 + 80
85t = 280
t = 280/85
t = 3.294 hrs, which is 3 + .294(60) = 3 hrs 18 min
then
the trains will meet: 3:00 + 3:18 = 6:18
:
;
Confirm this solution by finding actual dist each train traveled
3.294 * 45 = 148.23 mi
1.294 * 40 = 51.76 mi (left 2hr later)
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total distance: 199 mi, close enough
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