Question

A person walks in a distance x northward, turns around and walks a distance 7.00x southward. if the total displacement of the person from his starting position is 400 m south. what was the total distance walked

Answer 1

The total distance covered by a person is $\boxed{533.3\text{ meter}}$.

Further explanation:  

Distance is a scalar quantity that is the total distance covered by an object during its motion.

Displacement is a vector quantity, which is the shortest distance from the initial point to the final point or we can say that how much the object change its position.

Given:

A person walks in a distance $x$ in the north direction and then he turn around and walked $7.00x$ in the south direction. The total displacement of the person from his starting position is $400\text{m}$ south.

Step 1:

First we calculate the value of $x$.

A person walks in a distance $x$ in the north direction and then he turn around and walked $7.00x$ in the south direction.

It means the actual position of person is $6.00x$ in south direction.

It can be mathematically expressed as,  

$x-7.00x=-6.00x$  

The displacement is the shorter distance from the initial point to final point.

Therefore, the displacement of the person is $6.00x$.

The given displacement is $400$ south.

Thus the value of $x$ is calculated as,

$\begin{aligned}6.00x&=400\\x&=\dfrac{400}{6.00}\\x&=66.66\end{aligned}$  

The value of $x$ is $66.66$.

Step 2:

Now we calculate the total distance covered by the person.

A person walks in a distance $x$ in the north direction and then he turn around and walked $7.00x$ in the south direction.

It means the total distance covered by the person is the sum of distance covered in north direction and the distance covered in the south direction.

It is mathematically expressed as follows:

$\begin{aligned}d&=x+7.00x\\&=8.00x\end{aligned}$  

Therefore, the distance is  as follows:

$d=8.00x$         …… (1)

Substitute $x=66.66$ in the equation (1) to calculate the total distance.

$\begin{aligned}d&=8\times66.66\\&=533.3\end{aligned}$

Therefore, the total distance covered by the person is $\boxed{533.3\text{ meter}}$.  

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Answer details:

Grade: Junior school

Subject: Mathematics

Topic: Direction sense

Keywords: Distance, motion, displacement, distance, direction, position, south direction, north direction, scalar, vector, actual position, initial point, final point.

Answer 2

Distance southward = 6x = 400, so x=66.66
total distance = 7x+x=8x = 533.33m