1. ## Trains

It takes a passenger train 3 hr less time than it takes a freight train to make a trip from Hughesville to Boggstown. The passenger train averages 63 km/h, while the freight train averages 42 km/h. Find the distance from Hughesville to Boggstown.

2. Originally Posted by junebug017
It takes a passenger train 3 hr less time than it takes a freight train to make a trip from Hughesville to Boggstown. The passenger train averages 63 km/h, while the freight train averages 42 km/h. Find the distance from Hughesville to Boggstown.
1. Let d denote the distance between the two cities.

From the definition of $\displaystyle speed=\dfrac{distance}{time}$ you know that

$\displaystyle time=\dfrac{distance}{speed}$

3. The passenger train needs: $\displaystyle t_P=\dfrac{d}{63}$

The freight train needs: $\displaystyle t_F=\dfrac{d}{42}$

4. If you add 3 hours to the time of the passenger train you'll get the time of the freight train:

$\displaystyle \dfrac d{63} + 3= \dfrac d{42}$

Solve for d.