Question

A man covers a distance \[14km\] in an hour partly on foot at the rate of \[4km/hr\] and partly on scooter\[44km/hr\]. Find the distance travelled by him on foot.

Answer 1

Hint: For solving this question we are given to find the distance travelled by man on foot. For that we have to form two equations based on the given equation and then we have to solve the two equations by substituting. Then we can find the value of x.

Complete step by step answer:
For the given question we are given to find the distance travelled by foot in the journey of \[14km\] and in 1 hr. In which he also covered some of the distance with a scooter.
Let us consider the distance covered by the man on the foot be \[x\].
Now, as we know the total distance is \[14km\] then the distance covered by the scooter will become \[14km-x\].
Let us consider the time taken to cover \[xkm\] (i.e. distance covered on foot) be \[t\].
As we know that the total time required to complete the whole journey is \[1hr\]. So, therefore time taken to cover \[\left( 14-x \right)km\] is \[\left( 1-t \right)hrs\].
As we know the formula
\[\text{speed=distance covered speed }\times \text{ time required to cover that distance}\]
By applying the above concept to the given problem, we will get two equations:
\[x=4.t\]
Let us consider the above equation as equation (1).
\[x=4.t...............\left( 1 \right)\]
\[14-x=44\left( 1-t \right)\]
Let us consider the above equation as equation (2).
\[14-x=44\left( 1-t \right)..............\left( 2 \right)\]
Substituting equation (1) in equation (2), we get
 \[\begin{align}
  & \Rightarrow 14-4t=44\left( 1-t \right) \\
 & \Rightarrow 14-4t=44-44t \\
 & \Rightarrow 40t=30 \\
 & \Rightarrow t=\dfrac{3}{4} \\
\end{align}\]
Therefore \[t=\dfrac{3}{4}\], now we have to find the distance travelled by man on foot which is equal to x and from equation (1), we get
\[\begin{align}
  & \Rightarrow x=4t \\
 & \Rightarrow x=4\left( \dfrac{3}{4} \right) \\
 & \Rightarrow x=3 \\
\end{align}\]

Hence, distance travelled by the man on foot is \[3km\].

Note: We can also solve this problem in another way i.e. we have to consider two equations based on the time. As we know the total time is \[1hr\]. We have to consider \[{{t}_{1}}\] and \[{{t}_{2}}\] as the time covered by foot and scooter and then we have to find two equations then by solving these two equations we can find the value of ‘x’.