How much longer?

Geometry Level 2

John is an athlete and is very enthusiastic about the sports meet to be held in his school a week from now. He usually runs on a circular track but now the authorities have shutdown the track. So john decides to go to the neighboring park which houses a square track. The diameter of the circular track which john previously used is equal to the side of the square track. If it took John 44 minutes to run around the circular track how many more minutes would it take for him to run along the square track ?

P.S. His speed is constant.


The answer is 12.

Milind Prabhu by milind prabhu , 21, India

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3 solutions

Milind Prabhu
Mar 13, 2014

The circumference of the field is π d \pi d where d is the diameter. The perimeter of the square field is 4 d 4d . John's speed is π d 44 m i n \frac { \pi d }{ 44min } . Time taken by john to run around the square field= d i s t a n c e s p e e d \frac { distance\quad }{ speed } = 4 d π d 44 m i n \frac { 4d }{ \frac { \pi d }{ 44min } } = 56 min. Therefore john took (56-44)=12 more minutes to go around the square field.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

I thought john ran through the circumference in approx.138 minutes and they told us 'side of a square track' so i multiplied 138 with 4 and it then should be 552 min and minus 44 min, so 508 min to complete the square field... :/

Hassaan Islam - 7 years ago
Srishti Agrawal
Apr 3, 2014

Circumference of circle is pie*d and speed = Distance/time and time is equal to 44 minutes . so, the velocity will come out to be d/14. and perimeter of square will be 4d and speed = distance upon time we equate to get t = 56 minutes .Extra time = 56 -44= 12 minutes.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Hello.... as diameter of a circle = side of a square, radius = diameter / 2

total distance travelled = 2 pie r = 2 x pie x diameter / 2 = pie x diameter,

as for a square, total distance travelled = 4 x diameter,

as for speed running around the circular track = pie x diameter / 44,

as for speed running around the square track = 4 x diameter / Time Taken,

mentioned that speed is constant,so by comparing,

pie x diameter / 44 = 4 x diameter / Time Taken

Time Taken = 4 x 44 x diameter / pie x diameter

Time Taken = 4(44) / pie = 176 / 22/7 =176 x 7/22 = 8 x 7 = 56 mins,

Therefore,it takes 56 minutes to complete the square track,

therefore,the remaining time is = 56 - 44 = 12 mins...

thanks....

0 Helpful 0 Interesting 0 Brilliant 0 Confused

nice try.....!

Agustin Peñalosa Jr. - 7 years ago

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