Jen runs from home to a park and back She runs an average of

Jen runs from home to a park and back. She runs an average of 6 mph from home to the park and 4 mph from the park to home. If the round-trip takes 5 hours, what is the distance, in miles, between the park and Jen

Solution

D=RT
D=6T FOR THE RUN TO THE PARK.
D=4(5-T) FOR THE RETURN RUN.
BECAUSE THE DISTANCES ARE THE SAME WE HAVE:
6T=4(5-T)
6T=20-4T
6T+4T=20
10T=20
T=20/10
T=2 HOURS FOR THE 6 MPH RUN.
D=6*2=12 MILES FROM HOME & THE PARK.
PROOF:
12=4(5-2)
12=4*3
12=12