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# If John traveled 9 miles on his unicycle, what was his speed in miles

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Math Expert
Joined: 02 Sep 2009
Posts: 61302
If John traveled 9 miles on his unicycle, what was his speed in miles  [#permalink]

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18 Sep 2018, 20:59
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Difficulty:

75% (hard)

Question Stats:

38% (01:14) correct 63% (01:18) wrong based on 88 sessions

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If John traveled 9 miles on his unicycle, what was his speed in miles per hour?

(1) The unicycle has spokes that stretch the 23 inches from the center of the wheel to inner edge of the wheel.
(2) John pedals his unicycle at 19 revolutions per minute.

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Joined: 20 Feb 2015
Posts: 724
Concentration: Strategy, General Management
Re: If John traveled 9 miles on his unicycle, what was his speed in miles  [#permalink]

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26 Sep 2018, 22:16
Bunuel wrote:
If John traveled 9 miles on his unicycle, what was his speed in miles per hour?

(1) The unicycle has spokes that stretch the 23 inches from the center of the wheel to inner edge of the wheel.
(2) John pedals his unicycle at 19 revolutions per minute.

distance = 9 miles = n*2 $$\pi$$r (where n is the number of revolutions made by the unicycle)
speed = $$\frac{distance}{time}$$ =$$\frac{9}{time}$$ = ?

(1) The unicycle has spokes that stretch the 23 inches from the center of the wheel to inner edge of the wheel.

we are given radius = 23 inches
substituting the value back into the equation 9 miles = n*2 $$\pi$$r will give us n (number of revs)
time =?

not sufficient

(2) John pedals his unicycle at 19 revolutions per minute.
again we are not given time

not sufficient

E
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Joined: 05 Sep 2016
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WE: Engineering (Energy and Utilities)
Re: If John traveled 9 miles on his unicycle, what was his speed in miles  [#permalink]

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27 Sep 2018, 00:20
1
Bunuel wrote:
If John traveled 9 miles on his unicycle, what was his speed in miles per hour?

(1) The unicycle has spokes that stretch the 23 inches from the center of the wheel to inner edge of the wheel.
(2) John pedals his unicycle at 19 revolutions per minute.

Fact:D=9 Miles, t=?, S=?
Question:Speed=Distance/Time=?

Condition1: The unicycle has spokes that stretch the 23 inches from the center of the wheel to inner edge of the wheel.
Please note it's given as inner edge. Not outer edge which would have given the exact circumference of wheel needed for calculation.
Not Sufficient.

Condition2: he moves at 19Revs/min= 1140 Revs/hr.
But not sufficient.

Condition (1)+(2): Circumference*revs/hr would give the distance travelled in 1 hour in inches/hr unit. Convert it to miles/in 1 hr. Divide 9 Miles/this figure to get the time.
BUT as stated in condition (1) Inner dia would not be accurate to solve this question, for this we need outer dia or circumference.

So, NOT SUFFICIENT.

ANS-E
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Joined: 08 Aug 2017
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Re: If John traveled 9 miles on his unicycle, what was his speed in miles  [#permalink]

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07 Dec 2019, 05:52
Speed = outer radius* rotational speed.

Rotational speed = 2*pi*N (N is number of revolutions.)

Statement 1 gives only inner radius
Statement 2 gives only rotational speed.

Intern
Joined: 30 Aug 2019
Posts: 7
If John traveled 9 miles on his unicycle, what was his speed in miles  [#permalink]

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08 Dec 2019, 06:02
I think the essence of this question is that you can calculate the perimeter of the wheel from its radius and multiple by the number of revolutions to arrive at the distance. However, the distance from the center to the inner edge of the wheel says gives us nothing because what we need is the OUTER edge of the wheel.
If John traveled 9 miles on his unicycle, what was his speed in miles   [#permalink] 08 Dec 2019, 06:02
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