I need help solving a problem.

Question

Red hacks into a scheduling main frame and makes adjustments to two train schedules.  Train A will leave Chicago at 1:00pm traveling to St Louis and Train B will leave St Louis at 1:30pm travelling towards Chicago on the same track.  The stations are 350 miles apart and both trains are traveling at 50 MPH.  At what time will the trains crash outside of a miracle.

Answer 1

Train A leaves 30 min before Train B, so let's deal with that first:

 

at 1:30, Train A will have traveled for 30 min (at a rate of 50mph, that is 25 miles, yes?) and Train B will not have left at all.

 

So the distance at 1:30 between Train A and Train B is 325 miles (350 - 25 = 325)

 

Both trains travel at 50 mph.  The general formula Distance = rate x time can be used to figure out how long it will take either train to travel the 325 miles (325 miles = 50 mph x time --> it takes 6.5 hours to travel 325 miles).

 

 

However, we don't want to know how long it will take for Train A or B to travel all of the 325 miles.  Because they are heading towards each other at the same rate, each will travel half of 325 miles, or 162.5 miles.  So, how long will it take the trains to travel 162.5 miles?  (half the distance, half the time! so 3.25 hours; or if you wanted to calculate it, 162.5 miles = 50 mph x time --> time = 3.25 hours)

 

3.25 hours is 3 hours and 15 minutes.  Since we started at 1:30, 3 hours and 15 minutes later is 4:45.

 

They'll collide at 4:45.