1.    = 82 .

     It is the sum of the two rates,  and .

     So, your first equation is 

      +  = 82.


2.  Your second equation is

      -  = 18.   ("The speed of the freight train is 18 miles per hour slower than the speed of the passenger train.")


3.  Combine these two equation to the system:

     +  = 82.
     -  = 18.


4.  Now add the two equations. You will get.

     = 82 + 18 = 100.

    Hence,   = 100.  

    Then       =  = 50  is the speed of the passenger train.

    Then the speed of the freight train is 50-18 = 32 .

Answer.  50 km/h for the passenger train and 32 km/h for the freight train.

Let speed of freight (slower) train be S

Then speed of passenger (faster) train = S + 18

We then get the following DISTANCE equation: 2.5S + 2.5(S + 18) = 205

2.5S + 2.5S + 45 = 205

5S = 205 - 45

5S = 160

S, or speed of freight (slower) train = , or 

Speed of passenger (faster) train = 32 + 18, or  

RELATED QUESTIONS

A freight train leaves a station and travels east at an average speed of 48 mph.  Later,... (answered by stanbon,greenestamps)

A passenger train leaves a train station on schedule. A freight train had departed from... (answered by Theo,greenestamps,MathTherapy)

A freight train leaves the station traveling at 30km/hr. One hour later, a passenger... (answered by TimothyLamb)

A freight train leaves a station and travels due east at a speed of 60 mph. One hour... (answered by Alan3354)

A freight train leaves a station and travels north at 50mph. One hour later, a passenger... (answered by rfer)

a freight train leaves a station and travels north at 55 mph. One hour later,  a... (answered by lwsshak3)

  At 7:30 pm. , a freight train leaves the station and travels east and a passenger train  (answered by lwsshak3)

a passenger train and a freight train leave the same station at the same time. passenger... (answered by fcabanski)

a freight train leaves a station and travels north at 60 mph. two hours later, a... (answered by josmiceli)