Question

The length and breadth of a playground are \[80m\] and \[35m\] respectively. How long will a boy take to go three times around the field, if he walks at a rate of \[1.5m\] per second?

Answer 1

Hint:To solve this question first we will calculate the total perimeter of the rectangle because the boy is completing the round around it. Then we multiplied that perimeter by three because the boy completed three rounds. And then we use the distance formula for calculating time because we have given distance and speed.

Complete step by step answer:
We have given a playground of length \[80m\] and breadth \[35m\]. We have to find the total time taken by a boy if the boy completes 3 rounds and he walks at the rate of \[1.5m\] per second. First, we are going to find the perimeter of the playground (which is in the form of the rectangle as shown in the figure) because the boy is moving on the boundary not covering the area.

The playground is in the shape of a rectangle so we use the formula of the perimeter of a rectangle.
The Perimeter of the playground is \[ = 2\left( {l + b} \right)\].
The Perimeter of the playground is \[ = 2\left( {80 + 35} \right)\]
On further calculating
The Perimeter of the playground is \[ = 2\left( {115} \right)\]
The Perimeter of the playground is \[ = 230\]

The boy complete three rounds of that playground so the total distance to be covered is \[ = 3 \times 230\]
Total distance covered is \[ = 690\]
Using the formula of distance, time and speed.
\[{\text{distance}} = speed \times time\]
On rearranging the formula and putting the given values.
\[time = \dfrac{{{\text{distance}}}}{{speed}}\]
\[\Rightarrow time = \dfrac{{{\text{690}}}}{{1.5}}\sec \]
On further calculation.
\[\therefore time = 460\sec \]

Therefore, the total time taken by a boy to complete three rounds of the ground is \[460\sec \].

Note:In this question the boy is moving around a playground so we will calculate the perimeter of the ground. And if we have to cover the total ground then we will calculate the area of the ground. To solve this question students must know all the formulas related to figures like perimeter and area.