A freight train leave A for B 175 miles away and travels at the rate or 31.5
mph. after 1.5 hours a train leaves B for A traveling at 21.5 mph. How many
miles from B will they meet?

Distance = rate×time.  Therefore:
When the train leaves B, the train that left A is already (31.5)(1.5) or
47.25 miles down the track toward B, so they are only 175-47.25 or 127.75 miles
apart then.  

Their approach rate is the sum of their rates or 31.5+21.5 or 53 mph.

Since , they will meet  hours after the train that left B started. 
So, since , it will have traveled 21.5× or
51.82311321 miles from B.

Checking:  The train that left A will have traveled an additional 
31.5× miles or 75.92688679 miles and when we add those
we get 127.75 miles.

Answer: 51.8 miles approximately

-------------------------

Here is another way to solve it.  Make this chart, filling in the
rates:

                  distance    rate    time
train leaving A               31.5         
train leaving B               21.5     

Let the time traveled by the train that left B be t.
Then the train that left A will have traveled t+1.5


                  distance    rate    time
train leaving A               31.5    t+1.5     
train leaving B               21.5     t

Fill in the distances using distance = rate×time

                  distance    rate    time
train leaving A  31.5(t+1.5)  31.5    t+1.5     
train leaving B    21.5t      21.5     t


The sum of the distances must equal 175, so

        31.5(t+1.5) + 21.5t = 175

      31.5t + 47.25 + 21.5t = 175

                53t + 47.25 = 175

                        53t = 127.75

                          t = 

                          t = 2.410377358 hours

The answer is the distance traveled by the train leaving B.

 21.5t = 21.5(2.410377358) =  51.8231132 miles.



Edwin