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Johan rides his bicycle to and from college everyday

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Johan rides his bicycle to and from college everyday [#permalink]

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New post 25 Apr 2017, 20:51
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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
[Reveal] Spoiler: OA

Kudos [?]: 158 [0], given: 77

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Re: Johan rides his bicycle to and from college everyday [#permalink]

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New post 25 Apr 2017, 22:01
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

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Re: Johan rides his bicycle to and from college everyday [#permalink]

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New post 29 Apr 2017, 09:04
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saswata4s wrote:
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


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
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Re: Johan rides his bicycle to and from college everyday [#permalink]

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New post 29 Jul 2017, 20:41
I have a small doubt the circumference and the rotation around the circle gives the same meaning right? Because when we say revolving around the circle we mean it is 1 rotation= going around the circumference. Is this not right??

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Johan rides his bicycle to and from college everyday [#permalink]

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New post 25 Sep 2017, 10:22
longhaul123 wrote:
I have a small doubt the circumference and the rotation around the circle gives the same meaning right? Because when we say revolving around the circle we mean it is 1 rotation= going around the circumference. Is this not right??


No, they are not the same in that circumference gives you the actual distance and rotations dictate the number of times the actual distance is multiplied. Circumference is constant, rotations change.

For e.g., if the wheel's circumference is 2 mts (just for the sake of understanding), if you moved from one point rotating that wheel 5 times, it means that you have moved 10 meters away from the point where you started. Hope I made sense.

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Johan rides his bicycle to and from college everyday   [#permalink] 25 Sep 2017, 10:22
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