Question 177426This question is from textbook Contemporary Precalculus
: A train leaves New York for Boston, 200 miles away, at 3:00 p.m. and averages 75 mph. Another train leaves Boston for New York on an adjacent set of tracks at 5:00 p.m. and averages 45 mph. At what time will the trains meet?
This question is from textbook Contemporary Precalculus
Answer by MathTherapy(10555)   (Show Source):
You can put this solution on YOUR website! Let distance traveled by the NY to Boston train to the “meeting point” be d
Then distance traveled by the Boston to NY train to the “meeting point” is 200 – d
Because the train from NY to Boston has a 2 hr head start, its time to get to the “meeting point” will be 2 hrs more than it takes the Boston to NY train to get to that “meeting point.” Therefore, NY to Boston train’s time, less 2 hrs equals Boston to NY train’s time.
And, because T = D ÷ S, then
And, because T = D ÷ S, then 
3d - 450 = 1,000 - 5d
8d = 1,450
d = 181.25
This means that the NY to Boston train covers 181.25 miles to the “meeting point,” and the Boston to NY train therefore covers 18.75 (200 – 181.25) miles to the “meeting point.”
Since the NY to Boston train covers 181.25 miles at an average speed of 75 mph, it takes 2.4166666(181.25 ÷ 75) hours, or 145 minutes, or 2 hours, 25 minutes to get the “meeting point.” Therefore, it will get to the “meeting point” at 5:25pm, since it left NY at 3:00pm.
Since the Boston to NY train covers 18.75 miles at an average speed of 45 mph, it takes .4166666(18.75 ÷ 45) hours, or 25 minutes to get to the “meeting point.” Therefore, it will get to the “meeting point” at 5:25pm, since it left Boston at 5:00pm.
As seen, the two meeting times (5:25pm) are equal.
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