Question

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?

Answer 1

mike speed = (1/6) mile/min
dan speed = (1/9) mile/min
t-1 = mike time
t = dan time
distance = rate * time = same for both
d = (1/6) (t-1) = (1/9)(t)
3 t -3 = 2 t
t = 3 minute
distance = 3/9 = 1/3 mile

Answer 2

ratemike=1/6 ratedan=1/9

distancemike=ratemike*time
distancedan=ratedan(time-1)
set these equal, and solve for time.
Then, use the first equation to find out how far mike traveled. time will be in minutes, distance in miles.