SOLUTION: A train leaves New York for Boston, 200 miles away, at 4:00 P.M. and averages 65 mph. Another train leaves Boston for New York on an adjacent set of tracks at 5:00 P.M. and average

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Question 846951: A train leaves New York for Boston, 200 miles away, at 4:00 P.M. and averages 65 mph. Another train leaves Boston for New York on an adjacent set of tracks at 5:00 P.M. and averages 75 mph. At what time will the trains meet? (Round to the nearest minute.)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
From 4 PM to 5 PM, the 1st train travels:
+d%5B1%5D+=+r%2At+
+d%5B1%5D+=+65%2A1+
+d%5B1%5D+=+65+ mi
Start a stopwatch when the 2nd train leaves
at 5 PM
Stop the stopwatch when they meet
Let +d+ = the distance the 2nd train
travels until they meet
Let +t+ = the time in hrs on the stopwatch when they meet
----------------------
Equation for 1st train:
(1) +d+-+65+=+65t+
Equation for 2nd train:
(2) +d+=+75t+
----------------
Substitute (2) into (1)
(1) +75t+-+65+=+65t+
(1) +10t+=+65+
(1) +t+=+6.5+
5 PM plus 6.5 hrs is 11:30 PM
at which time they meet
-----------------------
check:
(2) +d+=+75t+
(2) +d+=+75%2A6.5+
(2) +d+=+487.5+
and
(1) +d+-+65+=+65t+
(1) +d+=+65+%2B+65%2A6.5+
(1) +d+=+65+%2B+422.5+
(1) +d+=+487.5+
------------------
According to these calculations, they will
not meet because 487.5 miles is greater than the
200 miles between NY and Boston
------------------------------
Another check is:
The 1st train takes
+t+=+200%2F65+
+t+=+3.077+ hrs to get to Boston
and
The 2nd train the 2nd train takes the 1 hr delay
plus +t+=+200%2F75+
+1+%2B+200%2F75+=+3.667+ hrs
So, the 1st train get there +3.667+-+3.077+=+.59+
hrs before the 2nd train, or about +.6%2A60+=+36+
36 minutes before the 2nd train
Hope I got it!