Question 124356
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r


Let t=time it takes cyclist to overtake runner AFTER the cyclist starts.
And t+1.33 hr=time that we are looking for
Distance runner runs before cyclist starts=2*1.33=2.66 mi

Total distance runner runs=2t+2.66
Total distance cyclist travels=4t

We know that the cyclist will have overtaken the runner whe they have both travelled the same distance.  So our equation to solve is:

2t+2.66=4t  subtract 2t froom both sides

2t-2t+2.66=4t-2t  collect like terms

2t=2.66  divide both sides by 2

t=1.33 hr 
t+1.33hr=1.33hr+1.33hr=2.66hr=2.7hr-------------------ans

CK
In 2.7 hr, runner runs2*2.66=5.32 mi
In 1.33hr cyclist travels 4*1.33=5.32mi

Hope this helps--ptaylor