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Perimeter

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by leonswati » Mon Apr 23, 2012 9:04 am
A circular running track is one mile long when measured along inside curb. Two athletes run one lap around the track. One runner stays one foot from curb and the other stays 6 feet from it during the entire lap.How many feet does the inside runner run than the outside runner? Express the answer in terms of "pi".?

My approach:

Radius of the track: 2* pi*r
Radius : 2640/pi

1st runner:
Radius = 1+(2640/pi)
perimeter = 5280+2pi

2nd runner:
Radius =6+(2640/pi)
Perimeter = 12pi + 5280

therefore extra mile that the outsider ran(but the question asks for the extra mile the insider ran)= 5280+12pi-5280-2pi= 10pi.


Am I doing something wrong... Plz help me solve it....
Swati
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by Shalabh's Quants » Mon Apr 23, 2012 10:24 am
leonswati wrote:A circular running track is one mile long when measured along inside curb. Two athletes run one lap around the track. One runner stays one foot from curb and the other stays 6 feet from it during the entire lap.How many feet does the inside runner run than the outside runner? Express the answer in terms of "pi".?

My approach:

Radius of the track: 2* pi*r
Radius : 2640/pi

1st runner:
Radius = 1+(2640/pi)
perimeter = 5280+2pi

2nd runner:
Radius =6+(2640/pi)
Perimeter = 12pi + 5280

therefore extra mile that the outsider ran(but the question asks for the extra mile the insider ran)= 5280+12pi-5280-2pi= 10pi.


Am I doing something wrong... Plz help me solve it....
How many feet does the inside runner run Less is missing than the outside runner? I think so? :|
Shalabh Jain,
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by leonswati » Mon Apr 23, 2012 10:33 am
Thanks for the reply. But is my approach correct.?
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by minhchau1986 » Mon Apr 23, 2012 11:00 am
Yours is correct. I got the same result

First we have 2*pi*r=5280 so R=2640/pi feet
First runner R(1)=2*pi*(2640/pi+1)=5280+2*pi
Second runner R(2)=2*pi*(2640/pi+6)=5280+12*pi

Difference of first runner and second runner is 10*pi

Is missing the Time of each runner? If we have the time, we can find out the speed of each runner, then we know how much feet each runner runs differently
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by Shalabh's Quants » Mon Apr 23, 2012 11:25 am
leonswati wrote:Thanks for the reply. But is my approach correct.?
Your approach is correct! there is no need to convert mile to feet. It all gets cancelled.

At last remains is 2.pie.6 - 2.pie.1 = 10.pie.
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