Question 104908
I'm not a great tutor here. Ican't show you any drawing. So, draw as I say:

Draw that Mary and Sue are apart. Mark that their 30 miles away form each other.(no need to be scaled).

If you overtake, this means that you reach the same point where  the other object/person is.

Let x= speed of Mary
____y= speed of Sue


Come to think of this fact: it is MARY who overtook. This means that Mary MUSt be FASTER than Sue!

After 6 hrs, they're at the same point. And take note: Sue is already ahead by 30 miles when they started. So,

_______________________{{{6x=6y+30}}}
_______________________{{{6x/6=(6y+30)/(6)}}}
________________________{{{x=y+5}}}

Now let's INVESTIGATE the second case: Mary and Sue heading toward each other.


They met in i hr. At that instant, the sum of the distance they had traveled is 30 miles.
So,

______________________{{{x+y=30}}}
But,
________________________{{{x=y+5}}}

Thus,
_______________________{{{(y+5)+y=30}}}
__________________________{{{2y+5=30}}}
____________________________{{{2y=25}}}
_____________________________{{{y=12.5}}}

Again,
________________________{{{x=y+5}}}

Then,
________________________{{{x=12.5+5}}}
________________________{{{x=17.5}}}


Therefore, Mary travels at a speed of 17.5 mph while Sue travels at the speed of  
12.5 mph!


Power up,
HyperBrain!