please solve

Question

its takes a passenger train 5 hr less time than it takes a freight train to make the trip from New york to Boston. The passenger train averages 76 km/h, while the freight train averages 38 km/h. Find the distance from New york to Boston.

 

How far is it from New York to Boston?

Answer 1

Let  P = # hours on passenger train for the trip

Let F = # hours on freight train for the trip

Since the passenger train takes 5 hours less than the freight train then P = F-5

 

The total distance is represented by distance = (rate)(time) or d = rt

In this case the rate of the distance the freight train travels is 38F

and the distance the passenger train travels is 76P

Since both are travelling the same distance we can equate the two giving

 

76P = 38F

Since P = F-5 we can substitute that back in to see how long the freight train takes for the trip

76(F-5) = 38F

76F - 380 = 38F

76F - 38F = 380

38F = 380

F = 380/38

F = 10

 

The freight train takes 10 hours to make the trip from New York to Boston

Since d = rt and the freight train travels at 38 km/hr we have a distance given by

d = (38 km/hr)(10 hr) = 380 km

 

The same distance should be found if we take P = F-5 and note that the passenger train takes 5 hrs to make the trip at a speed of 76 km/hr giving

d = (76 km/hr)(5 hr) = 380 km

 

As expected the distances are the same and the distance from New York to Boston is 380 km