Willie drove to his cabin on the lake and back. it took one hour longer to go there than it did to come back. the average speed on the trip there was 30 miles per hour. the average speed on the way back with 36 miles per hour. how many hours did the trip there take?

Distance to the cabin is  'D' .

                     Distance = (speed) x (time)

Distance going            =     30            H
Distance coming back =     36        (H - 1)

Distance is the same in both directions.

                                        30H  =  36(H - 1)

Eliminate parentheses:    30H         =  36H - 36

Add  36  to each side:      30H + 36 = 36H

Subtract  30H  from each side:   36 =   6H

Divide each side by  6 :                6 =     H

It took 6 hours to go, 5 hours to come back,
and the trip was 180 miles each way.

         6 x 30 = 180
         5 x 36 = 180                yay !

Notice that  180  is the least common multiple (LCM)
of  30  and  36 .  I'll bet that could have helped us if
we were all wide awake when we read the question.