Algebra word problem

[burleygirl]

I am trying to make sure I am on right track to helping my daughter with this problem. 

 

Two runners are on a track running in opposite directions at constant speeds.  Runner A takes 40 seconds to run a lap.  Runner B is going in the opposite direction.  They meet every 15 seconds. How long does it take Runner B to run a lap.  

 

I calculated the rate at 40 sec/15 sec = 2 2/3 times so I multiplied that by Runner A's 40 sec.  Is this on the right track?

 

 

[regentrude]

I do not understand your solution at all. Runner B can not possibly take a longer time than runner A, since that would cause them to meet less frequently than every 40/2 seconds.

Here is my solution:

let us start from the first time they meet.

in the next 15 seconds to the next meeting, runner A is covering 15/40 of the length of the track.

This means that runner B must have covered the other 25/40 of the length of the track.

The ratio of the speeds is thus Va/Vb=15/25

The ratio of the times for one lap is the inverse ratio of the speeds: Tb/Ta=va/vb=15/25=3/5

Tb=3/5 TA= (3/5)*40s= 24 s

[burleygirl]

Regentrude,

 

Thank you.  I should know how to do this but was having a brain fog.  Your answer makes sense.