A train leaves the station at noon. The train is 180 miles from its destination at 12:45 p.m. and 90 miles from its destination at 2:15p.m. How far is the station from its destination? At what time will the train reach the destination?

Question

A train leaves the station at noon.  The train is 180 miles from its destination at 12:45 p.m. and 90 miles from its destination at 2:15p.m.  How far is the station from its destination?  At what time will the train reach the destination?

mathmale · Answer

It may help if you represent 12:45 p.m. as 12.75, Noon as 12.00, and 2:15 p.m. as 14.25  (Note:  In Europe, 2:15 p.m. would be written as 1415.  15 minutes = 0.25 hour.)
We assume that the train's speed is constant.

mathmale · Answer

Complicated problem.  I've reached some conclusions, but it was slow going.

I'd suggest you use the formula d=rt (distance=rate times time) and its variations:

d=rt
r=d/t
t=d/r

mathmale · Answer

First of all, I wanted to figure out the train's speed.

Over the time interval 12:45 to 2:15 (which is 1.5 hours), the train covered 90 miles (as it started out 180 miles from its destination and then, 1.5 hours later, was 90 miles from its destination).  Therefore, the speed was r=d/t, or (here), r=90 miles / 1.5 hours = 60 mph.

We assume that this speed is constant.

Next, I wanted to figure out the arrival time.  Since the train was 90 mi from its destination at 2:15 p.m. (2.25 hours), and since its speed was 60 mph, the remaining travel time to its destination was 

t=d/r      which in this case     was   t  90 mi / 60 mph    = 1.5 hours.

This is 1.5 hours AFTER 2:15 p.m.  What time will the train arrive at its destination?

Can you now figure out how far the destination is from the starting point?  Hint:  What time did the train leave the station?  What time did the train arrive?  How long did it take to get from station to destination?

anonymous · Answer

Thanks! I think I got it now.

mathmale · Answer

My greaet pleasure.  More power to you!