Brenda and Sally run in opposite directions on a circular track,starting at diametrically opposite points. They first meet after Brenda has run 100 meters.They next meet after Sally has run 150 meters past their first meeting point.Each girl runs at a constant speed.What is the length of the track in meters?
(A) 250 (B)300 (C) 350 (D)400 (E) 500
Method 1:
Let the length of the track be x.
On the first meet, Brenda has run 100 meters, so Sally runs x/2-100.
They next meet after Sally has run 150 meters past their first meeting point. So at the same time Brenda runs x-150.
Each girl runs at a constant speed. So the ratio of distance that two people run is fixed.
100/(x/2-100)=(x-150)/150
x=350
Method 2:
The first time they met, they ran half a lap. The next time they met, they ran a lap.
Each girl runs at a constant speed. So the second time is twice as long as the first time.
So Brenda ran 200 meters for the second time.
So the length of a circle is 150+200=350 meters.