Question

A dog is walking at a speed of $6{\text{km}}/{\text{hr}}\;$. How much distance does it cover in 5 minutes?

Answer 1

Hint: Given that the dog is walking at a speed of $6{\text{km}}/{\text{hr}}\;$. Speed is calculated as $\dfrac{\text{distance}}{\text{time}}$, which gives, $\text{Distance}=\text{speed}\times \text{time}$ and time is $\dfrac{\text{distance}}{\text{speed}}$. Speed is given in kilometres per hour, convert it into metres per second. Using the speed and distance given, find the distance covered by the dog in 5 minutes.

Complete step-by-step solution:
We are given that a dog is walking at a speed of $6{\text{km}}/{\text{hr}}\;$. We have to calculate the distance it would cover in 5 minutes. We know that,
$\begin{align}
  & \text{Speed}=\dfrac{\text{distance}}{\text{time}} \\
 & \text{Distance}=\text{speed}\times \text{time} \\
\end{align}$
The dog can walk 6km in one hour. Convert the speed in terms of metres per second.
1 kilometre is equal to 1000 metres and 1 hour is equal to 3600 seconds.
$6\dfrac{\text{km}}{\text{hr}}=6\times \dfrac{\text{1000m}}{\text{3600sec}}=6\times \dfrac{\text{5m}}{\text{18sec}}=\dfrac{15}{9}{\text{m}}/{\text{sec}}\;$
The dog can walk $\dfrac{15}{9}$ metres per second. We have to calculate the distance for 5 minutes. 5 minutes is equal to 300 seconds because 1 minute is equal to 60 seconds.
$\text{time}=\dfrac{\text{distance}}{\text{speed}}$
Distance = ?
Time = 300 sec
Speed = $\dfrac{15}{9}{\text{m}}/{\text{sec}}\;$
$\Rightarrow \text{distance}=\dfrac{15}{9}\times 300=\dfrac{4500}{9}=500\text{m}$
Therefore the dog walks for 500 metres which can be said as half a kilometre and 1 kilometres is equal to 1000 metres.

Note: When a speed is given in ${\text{km}}/{\text{hr}}\;$, to convert it to metres per second, just multiply $\dfrac{5}{18}$ to the given speed value. And when speed is given in ${\text{m}}/{\sec }\;$ then multiply this by $\dfrac{18}{5}$ to the given speed value. So, do not get confused with metres and vice-versa.