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

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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

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

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

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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

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

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

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

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
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Re: A circular jogging track forms the edge of a circular lake that has a [#permalink]
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Kimberly77 wrote:
BrentGMATPrepNow 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

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

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

You definitely should not use the area of a circle formula for this question.
You were lucky because the radius of the circle is 1, and 1^2 = 1

It makes perfect sense for a person to walk a certain length (aka distance, aka circumference).
However, it makes no sense for a person to walk a certain area.
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