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# A circular jogging track forms the edge of a circular lake that has a

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A circular jogging track forms the edge of a circular lake that has a [#permalink]

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Updated on: 18 Oct 2015, 09:49
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A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?

A. 0.5< t < 0.75
B. 1.75< t < 2.0
C. 2.0 < t < 2.5
D. 2.5 < t < 3.0
E. 3 < t < 3.5

Originally posted by novice12 on 18 Oct 2015, 09:41.
Last edited by Bunuel on 18 Oct 2015, 09:49, edited 2 times in total.
Renamed the topic and edited the question.
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Re: A circular jogging track forms the edge of a circular lake that has a [#permalink]

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18 Oct 2015, 10:11
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Diameter =2
Circumference = 2 pi * 1 = 2 pi
Speed = 3 miles/ hour
Time , t= Distance / Speed
t = 2 pi / 3 = 2* 3.14 / 3 = 2* 1.05 = 2.10 approx
2.0< t < 2.5
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Re: A circular jogging track forms the edge of a circular lake that has a [#permalink]

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18 Oct 2015, 13:19
D=2, and R=1
circumference thus is 2pi miles
we know that she walked 3mph
knowing the formula rt=D, we can deduce that t= D/r
D is 2pi miles and r is 3mph
t = 2pi/3
pi can be rewritten as 22/7
2*22/7 = 44/7 and multiply this by 1/3 = 44/21. This is greater than 2, but less than 2.5, therefore, 2<t<2.5. Answer choice C.
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A circular jogging track forms the edge of a circular lake that has a [#permalink]

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09 Sep 2017, 07:12
novice12 wrote:
A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?

A. 0.5< t < 0.75
B. 1.75< t < 2.0
C. 2.0 < t < 2.5
D. 2.5 < t < 3.0
E. 3 < t < 3.5

Diameter of circular lake $$= 2$$ miles

Diameter $$= 2r$$ ------- ($$r$$ is the radius of circular lake)

Circumference of circular lake $$= 2\pi$$$$r$$ $$= 2\pi$$

Average speed $$= 3$$ miles/hour

$$Time (t)= \frac{distance}{speed} = \frac{Circumference}{speed} = \frac{2\pi}{3}$$ ---------- (we can approximate value of $$\pi$$ to $$3.1$$)

Time $$(t) = \frac{2*3.1}{3} = \frac{6.2}{3} = 2.0666$$

$$2.0666$$ comes between $$2.0$$ and $$2.5$$. Therefore $$2.0 < t < 2.5$$

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Re: A circular jogging track forms the edge of a circular lake that has a [#permalink]

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04 Apr 2018, 14:15
Diameter = 2 miles
Circumference of the lake = 2.pi.r = 2r.pi = D.pi = 2.pi

t = (circumference) / avg speed = (2.pi) / 3 = (2/3).pi

Now, pi = 22/7, therefore, t = (2/3).(22/7)

To make the multiplication easy - let's change the value of 22 to 21 in one case, and 24 in the other.

* When we change it to 21, then t > (2/3).(21/7) = 2
* When we change it to 24, then t < (2/3).(24/7) = 16/7 = ~2.27

Therefore, 2.0 < t < 2.27 --- the only answer that fits this is C
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Re: A circular jogging track forms the edge of a circular lake that has a [#permalink]

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10 Apr 2018, 11:15
novice12 wrote:
A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?

A. 0.5< t < 0.75
B. 1.75< t < 2.0
C. 2.0 < t < 2.5
D. 2.5 < t < 3.0
E. 3 < t < 3.5

If the lake has a diameter of 2 miles, then its circumference (which is the length of the track) is 2 x π = 2π miles long. Since Johanna’s speed is 3 miles per hour, then the time it took her to walk around the lake is 2π/3 hours. Since π ≈ 3.14, so 2π/3 ≈ 6.28/3 ≈ 6.3/3 = 2.1 hours.

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Re: A circular jogging track forms the edge of a circular lake that has a [#permalink]

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12 Apr 2018, 06:09
novice12 wrote:
A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?

A. 0.5< t < 0.75
B. 1.75< t < 2.0
C. 2.0 < t < 2.5
D. 2.5 < t < 3.0
E. 3 < t < 3.5

Diameter = 2 miles

Distance = Circumference = 2 * pi * r = 2 * 3.1 * 1

Circumference = 6.2 miles approx.

Speed = 3 miles/hr

Time = 6.2/3

Time = 2.06 approx

Hence (C)
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Re: A circular jogging track forms the edge of a circular lake that has a   [#permalink] 12 Apr 2018, 06:09
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