a passenger train and a freight train leave a town at the same time and travel in opposite directions. Their speeds are 75 mph and 60 mph respectively. How long will it take for the trains to be 567 miles apart?

Step-by-step explanation: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.