Answer
64.8k+ views
Hint: Speed is defined as the distance covered by any object divided by the time taken to cover that distance.
Where Distance is the total length of the path covered by that object.
\[Speed = \dfrac{{Distance}}{{Time}}\]
Complete step-by-step answer:
Given, Farmer goes from point A to B
Then,
\[\begin{array}{*{20}{l}}
{Distance{\text{ }}AB{\text{ }}\left( S \right){\text{ }} = {\text{ }}61{\text{ }}km} \\
{Total{\text{ }}Time{\text{ }}taken{\text{ }}to{\text{ }}travel{\text{ }}61{\text{ }}km{\text{ }}\left( T \right){\text{ }} = 9{\text{ }}hours} \\
{Speed{\text{ }}at{\text{ }}which{\text{ }}farmer{\text{ }}travels{\text{ }}on{\text{ }}foot{\text{ }} = {\text{ }}4{\text{ }}km/hr} \\
{Speed{\text{ }}at{\text{ }}which{\text{ }}farmer{\text{ }}travels{\text{ }}on{\text{ }}bicycle{\text{ }} = {\text{ }}9{\text{ }}km/hr}
\end{array}\]
![](https://www.vedantu.com/question-sets/614b51c2-c452-4ac9-96a0-7d0e3a413e245516243054560301462.png)
Let the distance travelled on foot and bicycle be AC and BC respectively.
\[\begin{gathered}
Let{\text{ }}the{\text{ }}time{\text{ }}for{\text{ }}which{\text{ }}farmer{\text{ }}travels{\text{ }}on{\text{ }}foot{\text{ }} = {\text{ }}x{\text{ }}hrs, \\
Then{\text{ }}time{\text{ }}for{\text{ }}which{\text{ }}farmer{\text{ }}travels{\text{ }}on{\text{ }}bicycle{\text{ }} = {\text{ }}\left( {9 - x} \right){\text{ }}hrs \\
\end{gathered} \]
We know that,
\[Distance = Speed \times Time\]
Then, \[AC = 4km/hr \times xhr = 4x\] eqn (i)
\[BC = 9km/hr \times (9 - x)hr = 81 - 9x\] eqn (ii)
Also, \[AB = AC + BC\]
Using value of AB, AC and BC
We get,
\[\begin{gathered}
61 = 4x + 81 - 9x \\
5x = 20 \\
x = 4km \\
\end{gathered} \]
By putting value of x in eqn (i) and eqn (ii) we get,
\[\begin{array}{*{20}{l}}
{AC{\text{ }} = {\text{ }}16{\text{ }}km} \\
{BC = {\text{ }}45{\text{ }}km} \\
{\therefore Distance{\text{ }}travelled{\text{ }}on{\text{ }}foot{\text{ }}by{\text{ }}farmer{\text{ }} = {\text{ }}16{\text{ }}km}
\end{array}\]
Hence option (C) is correct
Note: Always check the unit of all the given data. For example, if the distance is given in km and speed is given in m/s then convert both the quantity into the same unit.
\[1{\text{ }}km{\text{ }} = {\text{ }}1000{\text{ }}m\]
\[1km/hr = \dfrac{5}{{18}}m/s\]
Where Distance is the total length of the path covered by that object.
\[Speed = \dfrac{{Distance}}{{Time}}\]
Complete step-by-step answer:
Given, Farmer goes from point A to B
Then,
\[\begin{array}{*{20}{l}}
{Distance{\text{ }}AB{\text{ }}\left( S \right){\text{ }} = {\text{ }}61{\text{ }}km} \\
{Total{\text{ }}Time{\text{ }}taken{\text{ }}to{\text{ }}travel{\text{ }}61{\text{ }}km{\text{ }}\left( T \right){\text{ }} = 9{\text{ }}hours} \\
{Speed{\text{ }}at{\text{ }}which{\text{ }}farmer{\text{ }}travels{\text{ }}on{\text{ }}foot{\text{ }} = {\text{ }}4{\text{ }}km/hr} \\
{Speed{\text{ }}at{\text{ }}which{\text{ }}farmer{\text{ }}travels{\text{ }}on{\text{ }}bicycle{\text{ }} = {\text{ }}9{\text{ }}km/hr}
\end{array}\]
![](https://www.vedantu.com/question-sets/614b51c2-c452-4ac9-96a0-7d0e3a413e245516243054560301462.png)
Let the distance travelled on foot and bicycle be AC and BC respectively.
\[\begin{gathered}
Let{\text{ }}the{\text{ }}time{\text{ }}for{\text{ }}which{\text{ }}farmer{\text{ }}travels{\text{ }}on{\text{ }}foot{\text{ }} = {\text{ }}x{\text{ }}hrs, \\
Then{\text{ }}time{\text{ }}for{\text{ }}which{\text{ }}farmer{\text{ }}travels{\text{ }}on{\text{ }}bicycle{\text{ }} = {\text{ }}\left( {9 - x} \right){\text{ }}hrs \\
\end{gathered} \]
We know that,
\[Distance = Speed \times Time\]
Then, \[AC = 4km/hr \times xhr = 4x\] eqn (i)
\[BC = 9km/hr \times (9 - x)hr = 81 - 9x\] eqn (ii)
Also, \[AB = AC + BC\]
Using value of AB, AC and BC
We get,
\[\begin{gathered}
61 = 4x + 81 - 9x \\
5x = 20 \\
x = 4km \\
\end{gathered} \]
By putting value of x in eqn (i) and eqn (ii) we get,
\[\begin{array}{*{20}{l}}
{AC{\text{ }} = {\text{ }}16{\text{ }}km} \\
{BC = {\text{ }}45{\text{ }}km} \\
{\therefore Distance{\text{ }}travelled{\text{ }}on{\text{ }}foot{\text{ }}by{\text{ }}farmer{\text{ }} = {\text{ }}16{\text{ }}km}
\end{array}\]
Hence option (C) is correct
Note: Always check the unit of all the given data. For example, if the distance is given in km and speed is given in m/s then convert both the quantity into the same unit.
\[1{\text{ }}km{\text{ }} = {\text{ }}1000{\text{ }}m\]
\[1km/hr = \dfrac{5}{{18}}m/s\]
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the common property of the oxides CONO and class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The area of square inscribed in a circle of diameter class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)