Raj leaves his house on his bicycle at an average speed of 10 miles per hour. his friend, ruth, leaves 1/2 hour later, following the same route and averaging 14 miles per hour. at what distance, in miles, from raj's house will ruth overtake him?

First set up equation for Raj, which is 10x + .5, .5 is the y-intercept because he got a head start of .5 hours
Ruth, 14x
10x + .5 = 14x
        - .5    -.5
10x          = 14x - .5
-14x           -14x
-4x  = -.5
/-4       /-4
   x = .125 miles
So she will overtake him at more than .125 miles
I hop this is right, and hope this helps