Ron get a 1.5 mile head start while running at a constant speed of 4.5mph. Bob runs a constant 10mph. How long will it take for Bob to catch-up with Ron?

Question

Ron get a 1.5 mile head start while running at a constant speed of 4.5mph. Bob runs a constant 10mph. How long will it take for Bob to catch-up with Ron?

Answer 1

At 4.5 mph, R has traveled 1/3 if an hour or 20 minutes, so he has a 20 minute lead over Bob.

 

So R is Ron's time and R-X is Bob's time. Now we have to decide how long it will have to take Bob to catch up so 4.5R and 10(R-20) have to be equal, i.e. they will both travel the same amount of time but at difference speeds

 

R*4.5 mph = (R - 20)* 10 mph

 

and we solve for R.

 

4.5E = 10R - 200

-5.5R = 200

R = -200 / -5.5 = 36.36 minutes