A passenger train and a freight train leave a town at the same time and travel opposite directions. Their speeds are 60 mph and 75 mph, respectively. How long w

Question

A passenger train and a freight train leave a town at the same time and travel opposite directions. Their speeds are 60 mph and 75 mph, respectively. How long will it tAKE FOR THEM TO BE 297 MILES APART?

Answer 1

We have two trains.  A passenger train (PT) travelling at 60mph and a freight train (FT) travelling at 75mph.  Since they are travelling in opposite directions, we can add their distances travelled to determine their distance apart.

 

           <========== PT

                                  |

                             FT ==========>

          |  Total Distance = PT + FT |

 

Let t be time in hours.

Distance = rate x time (t)

PT rate = 60 mph (given)

FT rate = 75 mph (given)

Distance Apart = 297 miles (given)

 

PT distance = 60t

FT distance = 75t

 

PT distance + FT distance = 297 miles

 

60t + 75t = 297     Add like terms t

135t = 297            Divide by 135

t = 2.2 hours

 

Therefore, in 2.2 hours the trains will be 297 miles apart.

Check:

 

PT distance 60t + FT distance 75t = 297 when t=2.2

60(2.2) + 75(2.2) = 297?

132 + 165 = 297?

297 = 297?  Check.

 

So in 2.2 hours, the passenger train will have travelled 132 miles in one direction and the freight train will have travelled 165 miles in the opposite direction for a total of 297 miles apart.