Question

How long will John to make a round of a circular field of radius $21m$ cycling at the speed of $8m/\sec ?$

Answer 1

Hint: In this problem we need to find the total time using the speed distance formula and the circumference of the circle is a distance here.
Circumference of the circle$ = 2\pi r$

Complete Step-by-step Solution
Given,
A man takes 21 m to cover a circular distance at speed of $8km/h$.
The time taken by the man who cycling at the speed of $8km/h$ on the circular field is $59.4\sec $
The formula for the circumference of a circle
$ = 2\pi r$
Where r is the radius of the circle.
To find the speed of the men cycling bike $speed = \dfrac{{{\text{distance}}}}{{time}}$
Put all the values in formula
$\pi = \dfrac{{22}}{7}$
Circumference of a circle
$
  2 \times \dfrac{{22}}{7} \times 21 \\
   = 2 \times 22 \times 3 \\
   = 132m \\
$
We obtain value in m covert in km
We know,
$1m = \dfrac{1}{{1000}}km$
Convert 132m into km
$
  132m = \dfrac{{132}}{{1000}}km \\
   = 0.132km \\
$
Distance he travel is $ = 0.132km$
Speed is $8km/h$
Put all the values in the formula
$
  8 = \dfrac{{0.132}}{{Time}} \\
  time = \dfrac{{.132}}{8} \\
  Time = 0.0165hr \\
$
Now convert hour into sec
We know,
$1hour = 3600\sec $
To convert hour into second, multiply above value.
$
  0.0165hr = 0.0165 \times 3600 \\
   = 59.4\sec \\
$
$\therefore $ The time taken by the man who cycling at the speed of $8km/h$ on circular field is $59.4\sec $

Note:
In this type of question, we have to think about all the possible cases and corner cases. If any of the possible cases are missed then we might end up with the wrong answer. We also have to note that we can use permutation and combination interchangeably with some extra steps.