Question

A takes 2 hours more than B to walk d km. If A doubles his speed, then he can make it in 1 hour less than B. How much time does B require for walking d km.?

Answer 1

Hint: If we want to solve this question, then we need to find the time taken by B to walk d km. First of all, we find out the speed of A with the initial condition of A taking 2 hours more than B to walk d km. Then we will find the speed of A with the second condition where A doubles his speed, after that, we will get two equations. When we compare these two equations, as a result we will find the time taken by B to walk d km. The formula used for finding the speed of A in this question is given below,
\[\text{speed}=\dfrac{\text{distance}}{\text{time}}\]

Complete step by step answer:
Let us assume that time taken by B to walk d km be x.
According to first condition,
Distance to be travelled \[=\text{d km}\]
Time taken by B to walk d km \[=\text{x hours}\]
Time taken by A to walk d km \[=(\text{x}+2)\text{ hours}\]
Speed of A \[=\dfrac{\text{distance}}{\text{time}}=\dfrac{d}{x+2}\] [Let us assume this equation to be equation (i)]
According to second condition,
Distance to be travelled \[=\text{d km}\]
Time taken by B to walk d km \[=\text{x hours}\]
Time taken by A to walk d km \[=(\text{x}-1)\text{ hours}\]
Speed of A \[=\dfrac{d}{x-1}\] [Let us assume this equation to be equation (ii)]
Now according to question,
Speed of A in first condition is double the speed of A in second condition,
So, comparing equation (i) and equation (ii), we get
\[\begin{align}
  &\Rightarrow 2\times \left( \dfrac{d}{x+2} \right)=\dfrac{d}{x-1} \\
 & \Rightarrow \dfrac{2}{x+2}=\dfrac{1}{x-1} \\
\end{align}\]
Now, after cross-multiplying, we get
\[\begin{align}
  &\Rightarrow 2\times (x-1)=x+2 \\
 & \Rightarrow 2x-2=x+2 \\
 & \Rightarrow 2x-x=2+2 \\
 &\Rightarrow x=4 \\
\end{align}\]

Hence, the time taken by B to walk d km is 4 hours.

Note: The most important thing which we need to remember in solving this question is the relation between speed, distance and time. If someone forgets this relation, then they will not be able to solve this question. Be careful while making the equations of the time taken by A to walk d km with respect to B, as this is also a crucial mathematical part of the question.