Question 106148

distance(d)=rate(r) times time(t) or d=rt;t=d/r and r=d/t
Let t=time that elapses after John leaves until he catches Martina
We know that when John leaves, Martina has already travelled 24*2 or 48 miles (d=rt)

Distance Martina has travelled when John catches her=48+24t

Distance John has travelled when he catches Martina=48t
Now we know that John will have caught up with Martina when they have both travelled the same distance.

So our equation to solve is:

48+24t=48t  subtract 24t from both sides

48+24t-24t=48t-24t  collect like terms

48=24t  divide both sides by 24

t=2 hrs---------------------time that elapses after John leaves until he catches Martina

We are also told that John leaves at 11:00AM.  
So 11:00AM plus 2 hours=1:00PM ---------time that John catches Martina

CK

48+24*2=48*2
48+48=96
96=96

Hope this helps---ptaylor