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A car is being driven on a road. Assuming that the car's wheels turn

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A car is being driven on a road. Assuming that the car's wheels turn  [#permalink]

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New post 28 Oct 2014, 08:26
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Tough and Tricky questions: Geometry.



A car is being driven on a road. Assuming that the car's wheels turn without slipping, how many full 360° rotations does each tire on the car make in 10 minutes?

(1) The car is traveling at 50 miles per hour.
(2) Each tire has a radius of 20 inches.

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Re: A car is being driven on a road. Assuming that the car's wheels turn  [#permalink]

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New post 03 Nov 2014, 04:53
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Bunuel wrote:

Tough and Tricky questions: Geometry.



A car is being driven on a road. Assuming that the car's wheels turn without slipping, how many full 360° rotations does each tire on the car make in 10 minutes?

(1) The car is traveling at 50 miles per hour.
(2) Each tire has a radius of 20 inches.


(1) The car is traveling at 50 miles per hour.

We do not know the circumference of the each tire!

They could be small as wolkswagen bubble tires (many rotations) or large as monstertruck tires (fewer rotations)

NOT SUFFICIENT

(2) Each tire has a radius of 20 inches.

We do not know the speed of the car!

Standing still = 0 rotations
The car is actually traveling = more than 0 rotations

NOT SUFFICIENT

(1) + (2)

Distance traveled = \(50 * \frac{1}{6} = \frac{50}{6} miles\)
Circumference of the each tire = \(20*2*pi = 40*pi inches\)

Rotations = \(\frac{50}{6} miles / 40*pi inches\) (You don't have to do the calculations!)

SUFFICIENT

OA is C

Sorry for the messy expressions, \(pi inches\) = 3,14 inches :-D
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Re: A car is being driven on a road. Assuming that the car's wheels turn  [#permalink]

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New post 31 Dec 2016, 03:30
Consider the RT = D formula (rate × time = distance).

D, the total distance traveled by the car, will be equal to C, the circumference of each tire, times N, the number of 360° rotations made by each tire. Thus, we can rewrite our formula as RT = C*N.

The question is asking us how many 360° rotations each tire makes in 10 minutes. In other words, it is asking us for the value of N when T = 10. We can rewrite our equation thus:

R(10) = C*N

N = R(10)/C

Clearly, in order to answer the question “what is N” we need to know both R and C.

(1) INSUFFICIENT: This only gives us R, the speed of the car.

(2) INSUFFICIENT: This gives us the radius of the tire, which enables us to find C, the circumference of the tire. Knowing C is not, however, sufficient to figure out N.

(1) AND (2) SUFFICIENT: Now that we know both R and C, we can figure out what N is from the equation N = R(10)/C.
The correct answer is C.
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Re: A car is being driven on a road. Assuming that the car's wheels turn  [#permalink]

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New post 19 Feb 2018, 06:54
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Re: A car is being driven on a road. Assuming that the car's wheels turn &nbs [#permalink] 19 Feb 2018, 06:54
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