SOLUTION: At 6am a train traveling at 50mph leaves Los Angeles for San Francisco. Three hours later a train traveling at 40mph leaves San Francisco for Los Angeles. What time will the trains

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Question 624949: At 6am a train traveling at 50mph leaves Los Angeles for San Francisco. Three hours later a train traveling at 40mph leaves San Francisco for Los Angeles. What time will the trains pass each other? Assume the distance between the two cities is 450 miles.
I need an equation set-up to be solved please. Thank-you!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
How much of a head start did the 1st train have?
+d%5B1%5D+=+50%2A3+
+d%5B1%5D+=+150+ mi
After this head start, start a stopwatch when the 2nd train leaves.
Now both trains will travel for the same amount of time until
they meet.
Let +d++ = distance that 2nd train travels
----------
Equation for 1st train:
(1) +%28450+-+d%29+-+150+=+50t+
Equation for 2nd train:
(2) +d+=+40t+
--------------
(1) +300+-+d+=+50t+
Substitute (2) into (1)
(1) +300+-+40t+=+50t+
(1) +90t+=+300+
(1) +t+=+3.333+ hrs
The trains will pas each other 3 hrs and 20 min after
6 AM or 9:20 AM
check:
(1) +%28450+-+d%29+-+150+=+50%2A%2810%2F3%29+
(1) +300+-+d+=+500%2F3+
(1) +d+=+900%2F3+-+500%2F3+
(1) +d+=+400%2F3+
(1) +d+=+133.333+ mi
and
(2) +d+=+40t+
(2) +133.333+=+40t+
(2) +t+=+3.333+
OK
Note that first car travels +450+-+133.333+=+316.666+ mi
which includes the head start