Apassenger train's speed is 60 mi/h, and a freight train's speed is 40 mi/h. the passenger train travels the same distance in 1.5 h less time than the freight train. how long does each train take to make the trip?

Wow !  Let's see now . . .

Let's say the passenger train takes ' P ' hours for the trip.
Then the freight train takes ' P + 1.5 ' hours for the same distance.

The speed of the passenger train is 60, so he covers ' 60P ' miles.
The speed of the freight train is 40, to he covers ' 40(p+1.5) ' miles.
But the distances are equal !

60P = 40(P + 1.5) . . . . . There's your equation !

Eliminate parentheses on the right side:

60P = 40P + 60

Subtract 40P from each side:

20P = 60

Divide each side by 20 :

P = 3

The passenger train takes 3 hours, and the
freight train takes (P+1.5) = 4.5 hours.

Check:

In 3 hours, the passenger train covers (3 x 60) = 180 miles .
In 4.5 hours, the freight train covers (4.5 x 40) = 180 miles .
It works.
yay !

I'm not sure exactly but my best guess would be 1/4