One hour after a hiker left a camp, a cyclist set out to catch up. If the hiker traveled 3 miles per hour and the cyclist travelled 6 miles per hour faster, how long will it take the cyclist to catch up with the hiker?

20 minutes. In one hour, the hiker has traveled 3 miles, therefore the cyclist must travel 3 miles to catch up. If the cyclist travels 6 miles per hour faster, that means he is traveling at 9mph. 9mph / 3 = 3. The cyclist must travel 1/3 of an hour, or 20 minutes, to catch up to the hiker.

D=rt

when the distances traveled are the same, they are at the same place (caught up)

the time that the cyclist travels in that distance is t

the times that the hiker travels in that distance is t+1 (1 hour head start)

if hiker rate=3mph

and cyclist=3+6=9mph, then find the distance

hikerdistance=hikderdistance

3 (t+1) = 9t

3t+3=9t

minus 3t

3=6t

divide both sides by 6

1/2=t

the answer is 1/2 hour after the cyclist left, or 1 and 1/2 hour after the hiker left