Question

Nagma runs around a rectangular park 180m long and 120m wide at the rate of 7.5km/hour. In how much time will she complete five rounds?
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Answer 1

$\frak{\huge{AnswEr :}}$

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Given Parameters :

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• Length of rectangular park = 180m.

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• Breadth of rectangular park = 120m.

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• Speed of Nagma = 7.5 km/hr.

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We have to find the how much time will Nagma complete in five rounds?

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⋆ Reference of diagram is given below :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 180 m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 120 m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

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We know that, if we are given with the length of rectangular park and the breadth of rectangular park, we have the required formula, that is,

$\\ \\ \sf{: \implies Perimeter_{(rectangle)} = 2(l + b)}$

Substituting all the given values in the formula, we get :

$\\ \sf{: \implies Perimeter_{(rectangle)} = 2(180 + 120)} \\ \\ \\ \sf{:\implies Perimeter_{(rectangle)} = 2(300)} \\ \\ \\ \sf{:\implies \boxed{ \frak{ \red{Perimeter_{(rectangle)} = 600}}}}$

Now,

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→ Distance travelled in one round = 600

→ Distance travelled in five round = 5 × 600

→ Distance travelled in five round = 3000m.

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Converting from meter to kilometre :

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→ Distance = 3000/1000

→ Distance = 3km.

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Finally,

We know that, if we are given with the distance and speed of Nagma, we have the required formula, that is,

$\\ \\ \sf{:\implies Time = \dfrac{Distance}{Speed}}$

Substituting the given values in the formula, we get :

$\\ \sf{:\implies Time = \dfrac{3}{7.5}} \\ \\ \\ \sf{:\implies Time = \dfrac{30}{75}} \\ \\ \\ \sf{:\implies \boxed{ \frak{ \pink{Time = 0.4}}}}$

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$\therefore\underline{\textsf{The time taken to complete five rounds by Nagama is \textbf{0.4 hour.}}}$

Answer 2

Answer:

Given :-

• Length of park = 180 m
• Width = 120 m
• Speed = 7.5 km/hr

To Find :-

Time taken in 5 round

Solution :-

As we know that

${\textsf{ \textbf{Perimeter = 2(l + b)}}}$

Perimeter = 2(180 + 120)

Perimeter = (2 × 180) + (2 × 120)

Perimeter = 360 + 240

Perimeter = 600 m

Now,

Distance travelled in 5 round = Perimeter × 5

Distance travelled in 5 round = 600 × 5

Distance travelled = 3000 m

Now,

Conversion of m into km

1000 m = 1 km

3000 m = 3 km

Now,

Time = Distance/Speed

Time = 3/7.5

Time = 30/75

Time = 6/15

Time = 0.4 hr

Diagram :-

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 180 m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 120 m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$