Question

The area of a rectangular field is 3584 m2 and its length is 64 m. A boy runs around the
field at the rate of 6 km/h. How long will he take to go 5 times around it?​

Answer 1

AnswEr :

$\bold{Given} \begin{cases}\sf{Area \:of \: Rectangular \:Field=3584 \: {m}^{2} } \\ \sf{Length=64 \:m}\\ \sf{Boy \:Speed = 6 \:Km/hr}\\ \text{How long it will take to go 5 times around it?}\end{cases}$

• Area of Rectangular Field is Equal to :

⇒ Area of Rectangle = Length × Breadth

⇒ 3584 m² = 64 m × Breadth

• Dividing Both term by 64 m

⇒ Breadth = 56 m

$\rule{300}{1}$

• Total Distance Travelled in 5 Rounds :

⇒ Total Distance = Perimeter × 5

⇒ Total Distance = [2 × (L + B )] × 5

⇒ Total Distance = [2 × (64m + 56m)] × 5

⇒ Total Distance = [2 × 120m] × 5

⇒ Total Distance = 240 m × 5

⇒ Total Distance = 1200 m

• Dividing it by 1000 to Convert into Km

⇒ $\tt Total\:Distance = \cancel\dfrac{1200}{1000}\:Km$

⇒ $\red{\tt Total\:Distance = \dfrac{6}{5} \:Km}$

$\rule{300}{2}$

• Total Time Taken to Travel this :

$\longrightarrow \tt Distance = Speed \times Time$

$\longrightarrow \tt \dfrac{6}{5}\:Km = 6 \:Km/hr \times Time$

$\longrightarrow \tt \dfrac{\cancel{6\:Km}}{5 \times \cancel{6\:Km}/hr} = Time$

$\longrightarrow \tt \dfrac{1}{5hr} = Time$

• Changing it into Minutes

$\longrightarrow \tt Time = \dfrac{1}{ \cancel5} \times \cancel{60}$

$\longrightarrow\large\boxed{\tt Time = 12 \:minutes}$

⠀

∴ Boy will take 12 min. to make 5 rounds.

Answer 2

$\huge\star{\green{\underline{\mathfrak{Answer :-}}}}$

12 minutes

$\huge\star{\green{\underline{\mathfrak{Explanation :-}}}}$

Given :-

• Area of the rectangular field = $3584 {m}^{2}$
• Length = 64 m
• Speed of the boy = 6 km/hr

To find :-

Time taken by him to go 5 times around it?

Solution :-

Area = Length × Breadth

So, 3584 = 64 × Breadth

Hence, Breadth = 3584 ÷ 64

So, Breadth = 56 m.

The boy runs total distance of , let it be x in a round.

So, as he takes 5 rounds, the total distance = 5x.

Distance covered in one round :-

Perimeter = 2 ( l+b )

= 2 ( 64 + 56 )

= 2 ( 120 )

= 240 m.

So, total distance = 5x = 5 × 240 = 1200 m = 1.2 km.

We know that, Speed = Distance/Time

Speed given is = 6 km/hr.

We need to find the time.

So, Time = Distance/Speed

= 1.2 / 6

= 0.2 hrs.

= 12 minutes

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