Question

Dinesh went from place A to place B and from there to place C. A is \[7.5\] km from B and B is \[12.7\] km from C. Ayub went from A to place D and from there to place C. D is \[9.3\] km from A and C is \[11.8\] km from D. Who traveled more and by how much?

Answer 1

Hint:
We are required to find who amongst Dinesh and Ayub traveled more distance and by how much. To do that we will compute their distances separately and then compare them. We will then calculate their difference.

Complete step by step solution:
First we will find the distance traveled by Dinesh. We are provided with the information that Dinesh went from place A to a place B, and from there to a place C. Place A is \[7.5\] km from place B, and place B is \[12.7\] km from place C. Based upon this information, let us first draw a diagram to understand the question better.

From the figure we can see that the distance travelled by Dinesh is equal to the distance \[AC\]. That means we are required to find \[AC\].
\[AC = AB + BC\]
We will substitute \[7.5\] for \[AB\], and \[12.7\] for \[BC\] in the equation \[AC = AB + BC\]. After this add the terms.
\[\begin{array}{l}AC = 7.5 + 12.7\\ \Rightarrow AC = 20.2\end{array}\]
Hence, the total distance traveled by Dinesh is \[20.2\] km.
Now we will find the distance traveled by Ayub now. We are provided with the information that Ayub went from place A to a place D, and from there to a place C. Place A is \[9.3\] km from place D, and place D is \[11.8\] km from place C. Based upon this information, let us first draw a diagram to understand the question better.

Now we can see from the diagram that the total distance traveled by Ayub is AC. That means we are required to find \[AC\]. To do that we will proceed as follows,
The total distance AC can be given as \[AC = AD + DC\].
We will now substitute \[9.3\] for \[AD\], and \[11.8\] for \[DC\] in the equation \[AC = AD + DC\] and add the terms.
\[\begin{array}{l}AC = 9.3 + 11.8\\ \Rightarrow AC = 21.1\end{array}\]
Hence, the total distance traveled by Ayub is \[21.1\] km.
Now, as we are required to find who has traveled more distance, we will compare the distances traveled by both of them. On comparing we see that, \[20.2 < 21.1\].
This means that Ayub has traveled more distance than Dinesh.
Since we are required to find how much extra distance has been traveled, we will calculate the difference of the distance traveled by Ayub and Dinesh respectively.
\[{\rm\text{Extra distance traveled}} = {\rm\text{Distance traveled by Ayub}}-{\rm\text{Distance traveled by Dinesh}} \\
\Rightarrow 21.1 - 20.2 \\
\Rightarrow 0.9\]

Hence, we can conclude that Ayub traveled more than Dinesh by \[0.9\] km.

Note:
Distance is a scalar quantity. Thus, distances are always added without taking the directions into the picture. This is the fundamental difference between distance and displacement. Displacement is a vector quantity. which refers to minimum distance between two points.