A train leaves New York for Boston, 200 miles away, at 5:00 P.M. and averages 60 mph. Another train leaves Boston for New York on an adjacent set of tracks at 4:00 P.M. and averages 55 mph. At what time will the trains meet?

Question

anonymous · Answer

So we need one frame of motion, lets use from Boston to New York. So for the first equation, if use 5 o clock as our start time, we have 55 + 55t, and for our second we have 145 - 60t as it is moving away from our referencing point (which is 145 miles away), we can solve by saying 55 + 55t = 145 - 60t, and solving for t. This yields 115t = 90. We get t =  0.7826086956521738, which we multiply to find the minutes because we solved in terms of hours, and our result is 46.95652173913. So we started at 5:00 PM so we add our time to that and our result is approximately 5:47 PM.