Question

a freight train from Boston to NY and a passenger train from NYc to Boston depart at 3:00.the speed of FT is 80 mph and PT's speed is 60mph. At what time will the trains pass each other

Answer 1

Suppose the distance between Boston and NYC=s miles. Let t be the time in minutes after 3.00. 80mph=1.33 miles per minute; 60mph is 1 mile per minute.

At t=0, let the positions of the trains, x_FT and x_PT, be x_FT=0 (distance from Boston) and x_PT=s, so after time t:

x_FT=4t/3, x_PT=s-t (negative because PT is coming towards Boston).

When the trains pass x_FT=x_PT=x, so 4t/3=s-t, 7t/3=s, so t=3s/7 minutes, and the distance x=4s/7 miles from Boston.

If s=187 miles, t=561/7=80.14 minutes or about 1hr 20.14min. So the trains would pass at approx 4:20 at about 106.86 miles out of Boston. (We haven't considered the unknown lengths of the trains.)