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25 Apr 2017, 20:51
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
79% (02:08) correct
21%
(02:25)
wrong
based on 242
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Johan rides his bicycle to and from college everyday, and the round trip takes 2 hours. If the radius of the front wheel is 30 cm and the wheel makes 30000 rotations over the course of round trip, then which of the following is closest to Johan's average speed?
(A) 2π km/hr
(B) 4π km/hr
(C) 9π km/hr
(D) 10π km/hr
(E) 12π km/hr
(A) 2π km/hr
(B) 4π km/hr
(C) 9π km/hr
(D) 10π km/hr
(E) 12π km/hr
29 Apr 2017, 09:04
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saswata4s
The total distance of the round trip is equal to the circumference of the wheel times the number of rotations over the course of the round trip. Since the radius of the wheel is 30 cm, the circumference is C = 2πr = 2 x π x 30 = 60π cm. Since the wheel makes 30,000 rotations over the course of the round trip, the total distance of the round trip is 60π x 30,000 = 1,800,000π cm. Since the round trip takes 2 hours and rate = distance/time, the rate is 1,800,000π/2 = 900,000π cm/hr.
Now we need to convert cm to km. Since 1 m = 100 cm, 900,000π cm = 9,000π m. Since 1 km = 1,000 m, 9,000π m = 9π km. Thus, the rate is 9π km/hr.
Answer: C
General Discussion
25 Apr 2017, 22:01
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Radius of the wheel in KM = 30/100000 = 3/10000
Total distance travelled in the to and fro journey = total number of rotations * circumference of the wheel
= 30000 * 2 * π * 3/10000
= 3 * 2 * π * 3 = 18π
Johan's average speed = Total distance travelled in the to and fro journey/Total time taken in the to and fro journey
= 18π / 2 = 9π km/hr
Answer is (C) 9π km/hr
Total distance travelled in the to and fro journey = total number of rotations * circumference of the wheel
= 30000 * 2 * π * 3/10000
= 3 * 2 * π * 3 = 18π
Johan's average speed = Total distance travelled in the to and fro journey/Total time taken in the to and fro journey
= 18π / 2 = 9π km/hr
Answer is (C) 9π km/hr
