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

Circumference of a circle = (pi)(diameter)
So, the distance around the circular lake = (pi)(2) miles.

Travel time = distance/speed
So, Johanna's travel time = (pi)(2) miles/3 mph ≈ 6.28/3 ≈ 2.1 hours

Answer: C
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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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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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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.

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

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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Normally you may take the circumference at half the width of the track, so 2 +(x) as dia and radius as 1+(x/2).

But here the first reason is that they don’t give the width of track. And second reason, which is also why they may have not given the width, is that the width is too small when you compare it to the dia of the lake. 2-3 m to 2*1610 m —— 3 to 3200
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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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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

2 concepts majorly used here.
1. Distance = Speed * Time
2. Circumference of the circle= 2*Pie*r

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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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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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

Circumference = length of track = 2*pi
3 * t = 2*pi
t = (2*pi)/3
t = (2*22/7) / 3
t = 44/21, so t is a bit more than 2

A good way to estimate and solve quickly is -
t = 2 pi / 3
We know that pi = 22/7 => approx 3 (21/7)
And 2/3*3=2. Since we estimated 22/7 to be 21/7, we know that 21/7<22/7, thus t will be slightly more than 2.
Thus, 2.0<t<2.5

chetan2u Bunuel JeffTargetTestPrep

While solving this question, I imagined 2 concentric circles. The question says "A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles."

So, lake has a diameter of 2 miles, Wouldn't the jogging track have a diameter of 2+x miles, where x is the width of the track?

How to find circumference: C= 2*pi or 3.14* radius

In this case C= roughly 6.28
D= r*t
D=6.28/ 3 miles
time=2.09 mph
Answer: C

I know it sounds silly, but how did you find \frac{2*3.1}{3} = \frac{6.2}{3} = 2.0666[/m] so quickly? I was stuck between choice (C) and (D). That final step of working that out was taking 10/20secs too long.

Hi BrentGMATPrepNow, Question state "Johanna walked once around the track " I understand it as one whole circle so used pi* r^2 to calculate and still arrive at the correct answer. Is there anything wrong with the reasoning as compared to using circumference? Thanks Brent