GMATPrepNow wrote:
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
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 =
3HThe 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:
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing -
Learn more