find the speed of each train

Question

the speed of a passenger train is 6 mph faster than the speed of a freight train. The passenger train travels 340 miles in the same time it takes the freight train to travel 310 miles.Find the speed of each train.

Answer 1

Let x = speed of freight train, so x + 6 = speed of passenger train.  

Distance = (rate)(time), so Time = (Distance)/(Rate).

 

Let T_f = time it takes freight train to travel 310 miles

     T_p = time it takes passenger train to travel 340 miles

 

We know that T_f = T_p, so 310/x = 340/(x+6).

 

Cross multiplying yields 310(x+6) = 340x

                                  310x + 1860 = 340x

                                             1860 = 30x

                                               62  = x

speed of freight train = x = 62 mph

speed of passenger train = x + 6 = 68 mph