Question

A runner and a walker depart from the same point going in opposite directions on a circular track that is 1 mile long. The runner travels at 9 mph and the walker at 3 mph. After how many minutes will they pass each other?

I know the answer is 5 but I don't know how to get it

Answer 1

let the time passed be t hrs
When they meet, let the faster have gone x miles
then the slower has gone 1-x miles

time of faster = x/9
time of slower = (1-x)/3

but, when they meet, each has gone the same time, so

x/9 = (1-x)/3
3x = 9 - 9x
12x = 9
x = 9/12

time of faster = (9/12) ÷ 9
= 1/12 hrs
or 5 minutes

Answer 2

or, consider that the walker covers 1/4 mile while the runner covers 3/4 mile.

(1/4 mi)/(3 mi/hr) = 1/12 hr = 5 min.