Question

Two men $A$ and $B$ starts from a place $P$ walking at $3km$ and $3.5km$ an hour respectively. How many kilometers will they be apart at the end of $3$ hours, if they walk in opposite directions?
A. $13.5km$
B. $15.5km$
C. $17.5km$
D. $19.5km$

Answer 1

Hint: We will first assume the distance traveled by the person $A$ who started from point $P$ and walking at $3km$ per hour as $x$. Now we will assume the distance traveled by the person $B$ who started from the same point $P$ but walking at $3.5km$per hour as $y$. Now we will create a diagram that represents the both persons and the directions of the persons. From the diagram we will calculate the required value.

Complete step-by-step answer:
We have been given that two men $A$ and $B$ starts from a place $P$ walking at $3km$ and $3.5km$ an hour respectively.
Let us take the distance covered by the person $A$ in $3$ hours as $x$.
If the person $A$ covers a distance of $3km$ in an hour, then the distance covered by the person $A$ in $3$ hours is given by
$\begin{align}
  & x=3kmph\times 3hour \\
 & x=9km \\
\end{align}$
Let us take the distance covered by the person $B$ in $3$ hours as $x$.
If the person $B$ covers a distance of $3.5km$ in an hour, then the distance covered by the person $B$ in $3$ hours is given by
$\begin{align}
  & y=3.5kmph\times 3hour \\
 & y=10.5km \\
\end{align}$
If the two persons travels in opposite directions, then we know that the diagram looks like below

Now the distance between the persons $A$ and $B$ is given by
$AB=x+y$
Substituting the values of $x$ and $y$ , then we will get
$\begin{align}
  & AB=9+10.5 \\
 & =19.5km \\
\end{align}$
Hence the distance between the two persons after $3$ hours is $19.5km$ if they travel in the opposite direction.

So, the correct answer is “Option D”.

Note: For this type of problem direction of the movement places a key role. Above we have found the distance when they travel in opposite directions. Now if they mentioned that they are travel in the same direction, then the diagram changed as


And the distance between them is given by
$\begin{align}
  & AB=y-x \\
 & =10.5-9 \\
 & =1.5km \\
\end{align}$
Hence the distance between them if they travel in the same direction is $1.5km$.