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Intern  Joined: 12 May 2013
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A circular jogging track forms the edge of a circular lake that has a  [#permalink]

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30 00:00

Difficulty:   25% (medium)

Question Stats: 74% (01:38) correct 26% (01:47) wrong based on 1025 sessions

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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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4
2
Diameter =2
Radius = 1
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
Answer 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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1
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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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 $$2.0 < t < 2.5$$

Answer (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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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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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.

Answer: 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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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

Radius = 1 mile

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]

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Diameter is 2. So radius is 1.

Time = Distance/Speed = 2*pi*1(Circumference)/3

Now pi = 3.14. So 3.14 / 3 is approximately one.

So t is greater than 2 but very near to 2
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Re: A circular jogging track forms the edge of a circular lake that has a  [#permalink]

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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

2 concepts majorly used here.
1. Distance = Speed * Time
2. Circumference of the circle= 2*Pie*r
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A circular jogging track forms the edge of a circular lake that has a  [#permalink]

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JeffTargetTestPrep wrote:
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.

Answer: C

Hi,

I imagined the lake and track as concentric circles. As a result I assumed a variable for the width of the circular track(as shown in the attached diagram) and messed up my calculations. Could someone please help me understand the flaw in my reasoning and what are the keywords that I should have paid more attention to in order to infer the scenario accurately.
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Re: A circular jogging track forms the edge of a circular lake that has a  [#permalink]

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brunel,

I am not understanding a thing. In a question like this, why are we assuming the width of the track to be negligible.

For example, the distance covered while walking around the lake is NOT equal to the distance covered while walking around the lake.

Or is it? Please help me understand.
Intern  Joined: 20 Aug 2018
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A circular jogging track forms the edge of a circular lake that has a  [#permalink]

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A video explanation can be found here:
https://www.youtube.com/watch?v=R1-NXvHWdxI

This is essentially a proportion question: 3 miles is to one hour as circumference is to t hours.

3/1 = C/t

The question tests whether you know the circumference formula, and whether we know that pi is approximately equal to 3.14
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Re: A circular jogging track forms the edge of a circular lake that has a  [#permalink]

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ovrup007 wrote:
Hi,

I imagined the lake and track as concentric circles. As a result I assumed a variable for the width of the circular track(as shown in the attached diagram) and messed up my calculations. Could someone please help me understand the flaw in my reasoning and what are the keywords that I should have paid more attention to in order to infer the scenario accurately.

Hey ovrup007,
I do not see any attached diagram,did you miss attaching one? Anyways,from what i understand from your quoted post is about considering width of track.I did the exact mistake while solving the question at first,when it appeared on my mock test.On closely checking the question stem ,we see:A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track.
SO here it is assumed that ,whatever the width of track is,she is walking on inside portion of track .Since there is no other way we could determine what the width of track is .Also the options don't have a exact number for the same reason-they have given a range.
So we can consider that she is walking on closest and the time taken is slightly greater than 2 and no other range overlaps or contains 2.If there is some width the the time taken will be more but that cannot be solved from given data.
Ans C
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If the post was useful,please send the kudos Re: A circular jogging track forms the edge of a circular lake that has a   [#permalink] 26 Dec 2018, 21:04
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