system of equations by elimination

Question

it takes a passenger train 5 hrs less time than it takes a freight train to make a trip from Hughesville to Rockville. The passenger train averages 76 km/h, while the freight train averages 38 km/h. Find the distance from Hughesville to Rockville.

 

 

How far is it from Hughesville to Rockville?

Answer 1

Let x = distance from Hughesville to Rockville

 

Distance = (Rate)(Time), so Time = Distance/Rate

 

Time of passenger train = Time of freight train - 5

 

x/76 = x/38 - 5

 

Multiply both sides by the LCD, 76:

 

x = 2x - 380

 

-x = - 380     So, x = 380 miles