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The area of the rectangular field is $3584\text{ }{{m}^{2}}$ and its length is $64\text{ }m$. A boy runs around the field at a rate of $6km/hr$. How long will he take to go 5 rounds around it?

Answer Verified Verified
Hint: Here we have to apply the formulas:
Area of the rectangle = length $\times $ breadth
Perimeter of the rectangle = 2(length + breadth)
Time = $\dfrac{\text{Distance}}{\text{speed}}$

Complete step-by-step answer:
Here, the area of the rectangular field is given as, $A=3584\text{ }{{m}^{2}}$
Length of the rectangular field is, $l=64\text{ }m$.
First, we have to find the breadth of the rectangular field, $b$.
We know the formula that the area of the rectangle,
$A=l\times b$
$3584=64\times b$
Therefore, by cross multiplication we get:
$\dfrac{3584}{64}=b$
By cancellation we get:
$b=56$
Hence, the breadth of the rectangle, $b=56$.
Next, we have to find the perimeter of the rectangular field, $P$. i.e.
$P=2(l+b)$
We have, $l=64$ and $b=56$. Therefore we get:
$\begin{align}
  & P=2(64+56) \\
 & P=2\times 120 \\
 & P=240 \\
\end{align}$
Hence, we got the perimeter of the rectangular field as, $P=240\text{ }m$.
We are given that the boy runs 5 rounds of field.
Therefore, the perimeter for 5 rounds = $240\times 5=1200\text{ }m$
It is also given that the speed of the boy running around the field, $S=6\text{ }km/hr$
The speed is given in $km/hr$, now we have to change it into $m/s$ by multiplying it with $\dfrac{5}{18}$.
Therefore, the speed,
$S=6\times \dfrac{5}{18}$
By cancellation we get:
$S=\dfrac{5}{3}m/s$
Next, we have to find the time required to cover 5 rounds of field, i.e. the time required to cover the distance of $1200\text{ }m$. Hence we get:
Time, $T=\dfrac{D}{S}$ , where $D$ is the distance and $S$ is the speed.
$T=\dfrac{1200}{\dfrac{5}{3}}$
We know that $\dfrac{a}{\dfrac{b}{c}}=\dfrac{ac}{b}$. Therefore, we get,
$T=\dfrac{1200\times 3}{5}$
By cancellation we get:
$\begin{align}
  & T=240\times 3 \\
 & T=720 \\
\end{align}$
We got time, $T=720$ seconds. Now we have to convert it into minutes by dividing it with 60.
$T=\dfrac{720}{60}$
By cancellation we get:
$T=12$ min
Hence, the time required to cover 5 rounds of field is 12 min.

Note: Here we have to calculate the perimeter of 5 rounds of field. So we have to multiply the perimeter by 5. In the question the unit is given in metre, so don’t forget to change the unit from $km/hr$ to $m/s$.