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In the figure above, car A and car B simultaneously begin traveling ar

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Math Expert
Joined: 02 Sep 2009
Posts: 48067
In the figure above, car A and car B simultaneously begin traveling ar  [#permalink]

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24 Dec 2014, 08:42
00:00

Difficulty:

55% (hard)

Question Stats:

74% (02:31) correct 26% (02:16) wrong based on 164 sessions

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Tough and Tricky questions: Geometry.

In the figure above, car A and car B simultaneously begin traveling around a circular park with an area of 1256 square miles. Both cars leave from the same point, the START location shown in the figure, and drive with constant speeds until they meet. Car A travels counter-clockwise at 40 miles/hour and car B travels clockwise at 60 miles/hour. Which of the following is closest to the number of minutes it takes the cars to meet?

A. 30
B. 40
C. 75
D. 125
E. 180

Kudos for a correct solution.

Attachment:

2014-12-24_1941.png [ 3.82 KiB | Viewed 3243 times ]

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Re: In the figure above, car A and car B simultaneously begin traveling ar  [#permalink]

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24 Dec 2014, 08:52
1
Area of the circle = pi X r^2
thus (22/7).r^2 = 1256
Solving we get r = 20
Circumference = 2 pi x r = 125.6 miles
the cars, since the travel towards each other, travel this distance in 40 + 60 = 100miles/ hr
Therefore they meet after 125.6/100 = 1.256 hrs = 75.6 mins

Hence C
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Re: In the figure above, car A and car B simultaneously begin traveling ar  [#permalink]

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24 Dec 2014, 11:47
1
Bunuel wrote:

Tough and Tricky questions: Geometry.

In the figure above, car A and car B simultaneously begin traveling around a circular park with an area of 1256 square miles. Both cars leave from the same point, the START location shown in the figure, and drive with constant speeds until they meet. Car A travels counter-clockwise at 40 miles/hour and car B travels clockwise at 60 miles/hour. Which of the following is closest to the number of minutes it takes the cars to meet?

A. 30
B. 40
C. 75
D. 125
E. 180

Kudos for a correct solution.

Attachment:
2014-12-24_1941.png

Area = 1256 miles = pi * r^2 ---> r=\sqrt{400} = 20 miles

Circumference of the park = 2 * Pi * r = 40*3.14 = 125.6 miles

total speed of the two cars = 100 miles

Time taken for both cars to meet = Distance/speed (hrs)
=1.256 hrs * 60
=75 mins(approximate)

Ans C
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Re: In the figure above, car A and car B simultaneously begin traveling ar  [#permalink]

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25 Dec 2014, 04:39
1
Took me 6 minutes to find the trick to avoid serious calculations.

1256=314*4.. Pie= 3.14 (approx)

pie*r sq= 1256 This will give R as 20.

Circumfrence of the circle is the total distance that the cars will travel= 2*pie*r=40* 3.14

since two cars are moving towards each other we can consider that 1 car is moving at speed of 100=60+40 miles while the other is stationary (Relative motion). Hence to meet the moving will cover the whole circumference of the circle.

Thus time =40*3.14/100 No need to calculate. This will be slightly more than 1.2 hrs. the only answer between 1 and 2 hrs is 75 minutes.

Math Expert
Joined: 02 Sep 2009
Posts: 48067
Re: In the figure above, car A and car B simultaneously begin traveling ar  [#permalink]

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08 Jan 2015, 07:50
Bunuel wrote:

Tough and Tricky questions: Geometry.

In the figure above, car A and car B simultaneously begin traveling around a circular park with an area of 1256 square miles. Both cars leave from the same point, the START location shown in the figure, and drive with constant speeds until they meet. Car A travels counter-clockwise at 40 miles/hour and car B travels clockwise at 60 miles/hour. Which of the following is closest to the number of minutes it takes the cars to meet?

A. 30
B. 40
C. 75
D. 125
E. 180

Kudos for a correct solution.

Attachment:
2014-12-24_1941.png

OFFICIAL SOLUTION:

(C) To visualize this question, think about a circle as just a line segment joined at its two ends. Let’s first cut the circle at the starting point and make it into a straight line. Notice that cars A and B are at opposite ends of the line traveling toward each other.

A [ ______________________ ] B

We know that the area of the circular park is 1256 square miles and that the area of a circle is equal to πr². So, 1256 = πr². Divide by 3.14, our approximation of π.

1256/3.14 = 400 = r².r = 20 miles.

Now, solve for the circumference of the park: C = 2πr. Plugging 20 into the equation, we get:C = 2 × 3.14 × 20 = 125.6 miles.

To calculate how long it takes to meet, combine the speeds of car A and car B to see how long it would take them to travel 125.6 miles.

Car A and car B are traveling toward each other at the rate of 40 + 60 = 100 miles per hour (because they are heading toward each other, we add their speeds together). At 100 mph, it will take them 1.256 hours to travel 125.6 miles and meet up.

Multiply 1.256 hours by 60 (because there are 60 minutes in one hour, and we are looking for the answer in minutes): 1.256 × 60, which is approximately 75 minutes.

The correct answer is choice (C).
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Re: In the figure above, car A and car B simultaneously begin traveling ar  [#permalink]

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17 Jun 2016, 02:20
distance the cars have to travel = circumference of the circle = 2pir
given area = pir^2=1256
r^2=1256*7/22 = 400
r=20
therefore distance = 2pir=40*22/7= ~126
time taken = relative distance /relative speed = 126/100 = 1.26 hours ~ 1 hour 15 minutes = 75 minutes
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Re: In the figure above, car A and car B simultaneously begin traveling ar  [#permalink]

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14 Sep 2017, 22:01
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