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

Answer: the distance between these two cities would be 120 mi