Let  = the distance the slower train had gone after 1 hour.
Let  = the distance the faster train had gone after 1 hour.



Then by the Pythagorean theorem



Let the rate of the slower train be r.
Then the rate of the faster train is r+20. 

Using 





So



becomes:







Divide thru by 2



Factoring:









We ignore the negative rate.

So the rate of the slower train is r = 60 mi/h

Therefore the rate of the faster train is r+20 = 60+20 = 80 mi/h

So you were right!  The answer is 80 mi/hr

Edwin