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a circular jogging track

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by LevelOne » Sun Jun 21, 2009 12:57 pm
A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Joanna walked once around the track at the average rate 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

I could only get as far as:

d=2; r=1
P=2pir=2pi
3*t=2pi

Where am I going wrong?

thanks
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Source: — Data Sufficiency |
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by yogami » Sun Jun 21, 2009 3:57 pm
You were on the right track t solving for t will give you t is 2.0 something. So the answer is C. Just substitute Pi to 22/7 in your equation
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c

by deltaforce » Tue Jun 23, 2009 8:25 am
2 * 22/7 = 44/7 = approx 6.3 miles

6.3/3 = approx 2.15 hours or (t)
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by MBAD » Fri Feb 17, 2012 4:55 pm
I too found estimation to be useful here, although I wasn't aware that Pi ~ 22/7

Based on Distance/Rate = Time, I arrived at 2(Pi)/3. Since Pi is slightly larger than 3, you can imagine the 3's cancelling out with a little bit more than the 2 left over. Therefore, I chose the answer that had the the range slightly over 2.

This approach may not have held up if the problem required greater precision.
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by Anurag@Gurome » Fri Feb 17, 2012 7:57 pm
Diameter of the lake = 2 miles
Circumference of the lake = pi * diameter = 2(pi)

Distance = speed * time
speed = 3 mph and let us assume the time = t
2(pi) = 3 * t
t = 2(pi)/3
We know pi is 3.14 approx, so t > 2 hrs

The correct answer is C.
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by Jeff@TargetTestPrep » Wed Jun 13, 2018 3:33 pm
LevelOne wrote:A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Joanna walked once around the track at the average rate 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, its radius is 1 mile, and its circumference (which is the length of the track) is 2 x π x 1 = 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, theno 2π/3 ≈ 6.28/3 ≈ 6.3/3 = 2.1 hours.

Answer: C

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