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Tricky speed-distance-time question

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Tricky speed-distance-time question

by Brent@GMATPrepNow » Mon Apr 03, 2017 6:40 am
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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

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by regor60 » Mon Apr 03, 2017 7:13 am
First, visualize the distances covered here.

Pretend Ann isn't moving. Clearly, when they first meet, Bea will have traveled half the circumference to meet her on the other side.

Likewise, when they meet for the second time, Bea will have to have traveled the full circumference to meet Ann again.

So, Bea will have traveled 3/2 of the circle.

Now, recognize that since the two are travelling towards each other, you can add their speeds and assume one isn't moving, so we can use our pretend scenario in reality.

Closing Speed = 25 + 10 kph = 35 kph

Time traveled is 3/2 hr

D = R*T so 3/2 * circumference = 35 * 3/2

Therefore, circumference = 35
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by Brent@GMATPrepNow » Tue Apr 04, 2017 6:16 am
Brent@GMATPrepNow wrote:Image
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....
Image
. . . 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....
Image
. . . 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

Cheers,
Brent
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