Question 1207770
Mike can run the mile in 6 minutes, and Dan can run the mile in 9 minutes. If Mike gives Dan a head start of 1 minute, how far from the start will Mike pass Dan? How long does it take?

Mike can run the mile in 6 minutes, speed = 1/6 mi /minute
 and Dan can run the mile in 9 minutes. = 1/9 mi /minute

Mike gives Dan a head start of 1 minute 
It means the Dan is nine miles ahead of mike  when Mike starts to run

So Mile has to catchup 9 miles . catchup distance = 1/9 miles
Catch up speed = 1/6-1/9= 1/18 miles / minute

d/r = t

catchup time = catchup distance / catchup speed

(1/9)/(1/18)= 2 minutes

Distance covered by Mike in 2 minutes: 1/6×2=2/6=1/3

Mike will pass Dan 1/3 miles from the start, and it will take him 2 minutes to do so.