Question

A dog is walking at a speed of \[6{\rm{km/hr}}\].
1) How much distance does it cover in 5 minutes?
2) How much time would it take to cover 200 meters?

Answer 1

Hint:
Here, we are required to find the distance and time covered by the dog in two different situations, given that the speed of the dog is \[6{\rm{km/hr}}\]. First, we will convert the given time into hours using the conversion formula. Then we will use the formula of distance, speed, and time to find the distance covered by the dog. Again we will convert the given distance into kilometer using the conversion formulas. We will then use the distance-time-speed formula to find the time taken by the dog in the second situation.

Formula Used:
\[d = s \times t\] where, \[d\] is the distance, \[s\] is the speed and \[t\] is the time taken.

Complete Step by Step Solution:
It is given that the dog is walking at a speed of \[6{\rm{km/hr}}\].
Hence, the speed of dog, \[s = 6{\rm{km/hr}}\]
Now, we are required to find the distance covered by that dog in 5 minutes.
Time taken \[ = 5\] minutes
As the speed is given in \[{\rm{km/hr}}\] so we will convert the time from minute to hour.
Now, as we know, \[1{\rm{hr}} = 60\] minutes
Hence, using unitary method, dividing both sides by 60, we get
\[ \Rightarrow \dfrac{1}{{60}}{\rm{hr}} = 1\] minute
Therefore, multiplying both sides by 5, we get
\[ \Rightarrow \dfrac{5}{{60}}{\rm{hr}} = 5\] minutes
Time taken\[ = \dfrac{5}{{60}}{\rm{hr}}\]
Here, substituting \[s = 6{\rm{km/hr}}\] and \[t = \dfrac{5}{{60}}{\rm{hr}}\] in the formula \[d = s \times t\], we get,
\[d = 6 \times \dfrac{5}{{60}}\]
Multiplying the terms, we get
\[ \Rightarrow d = \dfrac{5}{{10}} = 0.5{\rm{km}}\]
Now, we know that \[1{\rm{km}} = 1000{\rm{m}}\].
So converting the distance to metre, we get
\[\begin{array}{l} \Rightarrow d = 0.5{\rm{km}} = \dfrac{5}{{10}} \times 1000\\ \Rightarrow d = 500{\rm{m}}\end{array}\]
Hence, the distance covered by the dog in 5 minutes is \[0.5{\rm{km}}\] or \[500{\rm{m}}\].
How much time would it take to cover 200 meters?
We know that,
Speed of dog, \[s = 6{\rm{km/hr}}\]
Distance to be covered \[ = 200{\rm{m}}\]
Now, we know that,
\[1{\rm{km}} = 1000{\rm{m}}\]
Hence, by using unitary method, dividing both sides by 1000,
\[ \Rightarrow \dfrac{1}{{1000}}{\rm{km}} = 1{\rm{m}}\]
Therefore, multiplying both sides by 200,
\[ \Rightarrow \dfrac{{200}}{{1000}}{\rm{km}} = 200{\rm{m}}\]……………………………..\[\left( 2 \right)\]
Here, substituting \[s = 6{\rm{km/hr}}\] and \[d = \dfrac{{200}}{{1000}}{\rm{km}}\] in the formula \[d = s \times t\], we get,
\[\dfrac{{200}}{{1000}} = 6 \times t\]
\[ \Rightarrow \dfrac{2}{{10}} = 6 \times t\]
Dividing both sides by 6,
\[ \Rightarrow t = \dfrac{2}{{10 \times 6}} = \dfrac{1}{{30}}{\rm{hr}}\]
Now we will convert the time into hours.
Now, \[1{\rm{hr}} = 60{\rm{min}}\]
Therefore, multiplying both sides by \[\dfrac{1}{{30}}\], we get
\[\begin{array}{l} \Rightarrow t = \dfrac{1}{{30}}{\rm{hr}} = \dfrac{{60}}{{30}}\\ \Rightarrow t = 2{\rm{min}}\end{array}\]
Hence, time taken is \[2{\rm{min}}\]or \[2 \times 60 = 120{\rm{seconds}}\]

Hence, time taken by the dog to cover 200 meters is \[2{\rm{min}}\]or \[120{\rm{s}}\]

Note:
When the speed is given in kilometers per hour, we can use the conversion formula to convert it into meters per second. We know that, \[1{\rm{km}} = 1000{\rm{m}}\], \[1{\rm{hr}} = 60{\rm{min}}\] and \[1{\rm{min}} = 60{\rm{s}}\]
Hence,
\[1{\rm{km/hr}} = \dfrac{{1000}}{{60 \times 60}}{\rm{m/s}}\]
\[ \Rightarrow 1{\rm{km/hr}} = \dfrac{5}{{18}}{\rm{m/s}}\]
Hence, we can use this formula directly to convert \[1{\rm{km/hr}}\] into meter per seconds. But, if we have to convert \[1{\rm{m/s}}\] into kilometers per hour, we will use the reciprocal of this formula, i.e. \[ \Rightarrow \dfrac{{18}}{5}{\rm{km/hr}} = 1{\rm{m/s}}\]