Ann and Bea are at opposite sides of a CIRCULAR track. At 12:00 pm

BTGModeratorVI wrote: ↑

Sun Sep 27, 2020 7:08 am

Ann and Bea are at opposite sides of a CIRCULAR track. At 12:00 pm, Ann starts traveling clockwise at a constant speed of 25 kilometers per hour. At the same time, Bea starts traveling counter-clockwise at a constant speed of 10 kilometers per hour. At 1:30 pm that same day, Ann and Bea cross paths for the SECOND time. What is the circumference (in kilometers) of the circular track?

A) 17.5
B) 35
C) 42
D) 52.5
E) 70

Answer: B
Source: GMAT prep now

Let's first calculate the TOTAL DISTANCE traveled by Ann and Bea combined.
Let's let H = HALF the circumference of the circle.

So, when they meet for the FIRST TIME....

. . . we can see that their combined travel distance = H (halfway around the circle).


Once they meet the first time, we can see that, when they meet for the SECOND TIME....

. . . we can see that their combined travel distance = 2H (from the time they met for the FIRST time).

So, the TOTAL distance traveled = H + 2H = 3H

The TOTAL travel time is 1.5 hours (noon to 1:30 pm)

Since Ann's speed is 25 kilometers per hour, and Bea's speed is 10 kilometers per hour, their COMBINED SPEED = 25 + 10 = 35 kilometers per hour

Since distance = (rate)(time), we can write: 3H = (35)(1.5)
Evaluate: 3H = 52.5
So, H = 17.5

In other words, HALF the distance around the circle = 17.5 kilometers.

So, the circumference of the circle = (2)(17.5) = 35 kilometers

Answer: B