Mary drove from amity to belleville at a speed of 50 mi/h. on the way back, she drove at 60 mi/h. the total trip took h of driving time. find the distance between these two cities.

Speed =distance  /  time 
Then:
distance=speed * time

Distance from Amity to Belleville =d₁
time=x
speed=50 mi/h

Distance from Belleville to Amity=d₂
time=4²/₅ h - x=(4+2/5)h-x=22/5h -x=4.4 h -x=4.4 -x
speed=60 mi/h

d₁=50 mi/h*x=50 x
d₂=60 mi/h*(4.4-x)=60(4.4-x)

d₁=d₂;  then_
50x=60(4.4-x)
50x=264-60x
50x+60x=264
110x=264
x=264/110=2.4

d₁=50 mi/h*(x)=(50 mi/h)(2.4 h)=120 mi

the distance between these two cities would be 120 mi