fozzzy
Brenda and Sally run in opposite direction 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
I am trying to explain my understanding:
As Brenda and Sally started diametrically opposite and started running towards each other (because, question mentions that they run in opposite direction), 1st time when they meet,
they meet at some point of the semi-perimeter of the circle.
Brenda ran 100meters.
Let us assume, Sally ran x meters.
So,the length of the semi-perimeter of the circular track is (100 + x) meters. Definitely, the full perimeter equals to (200+2x) meters.
Brenda and Sally are running in constant speeds (different but constant i.e. their speed did not change for the complete race). So, we can derive a ratio of distance covered by each, from 'speed is proportional to distance covered'. This means Sally and Brenda, each will cover the distances in the same ratio as respective speeds are constant.
so, the ratio =[the distance covered in the semi circle by Brenda] : [the distance covered in the semi circle by Sally] = 100 : x.
Now, coming to the 2nd time meeting, starting point is the point where they met 1st time.
So, to meet again, Brenda and Sally
together must cover the complete circumference i.e. (200 +2x) meters.
Sally covers = (200+2x)*[x/(100+x)] = 2x which is equal to 150 as question states.
So complete track length = circumference of the circle = 200 +2x = 200 +150 = 350 meters[Option C].
Please give kudos, if the explanation helps you.