Jessica and Lauren live on a straight road that runs east to

Jessica and Lauren live on a straight road that runs east to west. Jessica lives 1 mile west of Lauren. One morning at 9:00 am, they both start running east. If Jessica runs 4.5 mph and Lauren runs 3.75 mph, at what time will Jessica catch up to Lauren?

Solution

Let both meet t hours after 9am.
Distance travelled by Jessica in t hours = 4.5t
Distance travelled by Lauren in t hours = 3.75t
The difference is 4.5t-3.75t = 1 mile
0.75t = 1
t = 1/0.75 hours
t = 1 1/3 hours
t = 1h 20m