Two trains problem

Question

The evil villain in an action movie is using a computer to control two trains traveling toward each other on the same track. If  his demands for ransom aren't met with "t" amount of time, the trains will crash , killing all on board ,  including the hero's true love. How long does the hero have to break the computer code and save all the passengers by conveniently diverting the trains onto different tracks at the last possible moment? And how far did the fastest train travel? The faster train is locked into a speed of 108 mph and the slower train is locked into a speed of 96 mph . They are 51 miles apart when the hero gets the call for help!

Answer 1

Since the trains are moving towards each other, each train's speed relative to the other train is

 

108 + 96 = 204 mph

 

Therefore they will crash in

 

51 miles / 204 mph = 1/4 hours = 15 minutes.

 

The hero has 15 minutes to save the passengers.

 

The faster train would have traveled

 

108 mph · 1/4 hours = 27 miles.