My friend sets out walking at a speed of $3$ miles per hour. I set out behind her $5$ minutes later at $4$ miles per hour. For how many minutes will my friend have been walking when I catch up to her?
In 5 minutes your friend travels for 1/12 of an hour at 3 mph = 3/12 mi = 1/4 mi
You walk at 4 mph...so....effectively, you are traveling at (4 -3) = 1 mph
Distance/ Effective Rate = (1/4)mi / ( 1 m/hr) = 1/4 hr = 15 minutes to catch her