Algebra quick question

Question

a passenger train and a freight train leave cities 320 miles apart and travel toward each other the passenger train is travelling 20 miles faster than the freight train find the speed of each train if they pass each other after 4 hours

Answer 1

distance = rate of speed times time traveled

320 =4(P+F) where F= freight train's speed and P = the passenger train's speed with P=F+20

320+4(F+20+F) = 4(2F+20) = 8F + 80

8F = 320-80= 240

F = 240/8 = 30 miles per hour for the Freight train

and P =30+20 = 50 miles per hour for the Passenger train

in 4 hours they go 30(4) + 50(4) = 120+200 = 320 miles combined