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M08-25

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:38
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Difficulty:

65% (hard)

Question Stats:

70% (01:36) correct 30% (02:08) wrong based on 128 sessions

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If the diameter of each of the car's wheels is 20 inches, what was the approximate average speed of the car in km/h if after the two-hour journey each wheel made 75,000 revolutions? (1 inch = 0.0254 meter)

A. 32
B. 41
C. 59
D. 74
E. 88
[Reveal] Spoiler: OA

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15 Sep 2014, 23:38
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Official Solution:

If the diameter of each of the car's wheels is 20 inches, what was the approximate average speed of the car in km/h if after the two-hour journey each wheel made 75,000 revolutions? (1 inch = 0.0254 meter)

A. 32
B. 41
C. 59
D. 74
E. 88

The wheel's radius in meters = $$\frac{20 \text{ inches } * 0.0254}{2} = 0.254 \approx 0.25$$ meters.

The wheel's circumference = $$2\pi(0.25) = 0.5\pi \approx \frac{3}{2} = 1.5$$ meters.

The distance in kilometers = $$75000*\frac{1.5}{1000} = 75*1.5 = 112.5 \approx 113$$ km.

The average speed in km/h = $$\frac{113}{2} = 56.5$$ km/h which is closest to choice C.

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16 Jun 2015, 07:42
Hi Bunuel,

I am having trouble understanding this problem visually. Based on the solution, I can see we calculated the distance that the "wheel" travel. However, we want to calculate the distance that the car travel. Are they the same? I draw out how the wheel rotate on paper and having trouble to think of these two distances are the same. Could you help me clear this out?
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16 Jun 2015, 09:44
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Tsuruga wrote:
Hi Bunuel,

I am having trouble understanding this problem visually. Based on the solution, I can see we calculated the distance that the "wheel" travel. However, we want to calculate the distance that the car travel. Are they the same? I draw out how the wheel rotate on paper and having trouble to think of these two distances are the same. Could you help me clear this out?

I thinks similar problems might help:
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at-the-same-time-sue-began-rolling-a-wheelbarrow-from-x-to-y-nancy-199350.html
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21 Feb 2016, 17:13
The way I skipped some of the math:

piD = Circumference = 20pi

20 * 75,000 *pi = 150(plus a lot of zeroes) *pi

.025 = (1/4) minus a couple of zeroes. So take away a couple of zeroes from the big number and divide by four and you get close to 20. 20*pi = close to 60

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21 Nov 2016, 20:58
poor quality question
Math Expert
Joined: 02 Sep 2009
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21 Nov 2016, 21:29
womsuko wrote:
poor quality question

Care to elaborate? Thank you.
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05 Mar 2017, 12:38
hie
Re: M08-25   [#permalink] 05 Mar 2017, 12:38
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