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A circular jogging track forms the edge of a circular lake that has a
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Updated on: 18 Oct 2015, 08:49
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73% (01:10) correct 27% (01:26) wrong based on 782 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
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Originally posted by novice12 on 18 Oct 2015, 08:41.
Last edited by Bunuel on 18 Oct 2015, 08:49, 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
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18 Oct 2015, 09:11
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
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18 Oct 2015, 12:19
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
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09 Sep 2017, 06:12
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 \(2.0 < t < 2.5\) Answer (C)..._________________ Please Press "+1 Kudos" to appreciate.



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Re: A circular jogging track forms the edge of a circular lake that has a
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04 Apr 2018, 13:15
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
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10 Apr 2018, 10:15
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. Answer: C
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Re: A circular jogging track forms the edge of a circular lake that has a
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12 Apr 2018, 05:09
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 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
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11 Jun 2018, 08:08
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
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29 Aug 2018, 10:47
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
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04 Nov 2018, 19:12
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
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11 Nov 2018, 00:01
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.



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A circular jogging track forms the edge of a circular lake that has a
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24 Nov 2018, 13:33
A video explanation can be found here: https://www.youtube.com/watch?v=R1NXvHWdxIThis 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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