Help with an Algebra problem?

Question

When Butch Cassidy left the hideout, the Sundance Kid was already 15 miles ahead. Sundance rode at 20 mph while Butch rode at 30 mph. How long did it take Butch to catch up with Sundance?

Answer 1

distance=rate*time

d=r*t

x=20*t for Sundance

x+15=30*t for Butch

x=20t implies x/20=t

substitute

x+15=30*(x/20)

x+15=1.5x after simplifying 30/20

15=1.5x-x

15=0.5x

150=5x

x=150/5

x=30 miles

substitute

30=20*t

t=30/20

t=1.5 hours

check: x+15=30*t, 30+15=30*1.5, 45=45