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Varun and Arun start from a fixed point. Varun moves 3 km north and turns right and then covers 4 km. Arun moves 5 km west and turns right and walks 3 km. What is the distance between Varun and Arun now?

Follow Varun and Arun's journey from a fixed point. Varun travels 3 km north, then right, covering 4 km. Arun moves 5 km west, turns right, and walks 3 km. Discover the distance between them now.

by Maivizhi A

Updated Mar 06, 2024

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Varun and Arun start from a fixed point. Varun moves 3 km north and turns right and then covers 4 km. Arun moves 5 km west and turns right and walks 3 km. What is the distance between Varun and Arun now?

Varun and Arun start from a fixed point. Varun moves 3 km north and turns right and then covers 4 km. Arun moves 5 km west and turns right and walks 3 km. What is the distance between Varun and Arun now? 

The distance between Varun and Arun now is 9 kilometers.

To find the distance between Varun and Arun, we can represent their movements on a coordinate plane. Let's assume they start from the origin (0,0).

Varun moves 3 km north and then turns right, which means he moves east.

So, his final position is (4,3).

Arun moves 5 km west and then turns right, which means he moves north.

So, his final position is (-5,3).

Now, we can use the distance formula to find the distance between these two points:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) = (4,3) and (x2, y2) = (-5,3)

Plugging in the values:

Distance = √((-5 - 4)^2 + (3 - 3)^2)

= √((-9)^2 + (0)^2)

= √(81 + 0)

= √81

= 9 km

So, the distance between Varun and Arun now is 9 kilometers. 

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Speed, Time and Distance in Mathematics 

In mathematics, the relationship between speed, time, and distance is often described using the formula:

Distance = Speed × Time

This formula represents the fundamental concept that distance traveled is equal to the product of the speed at which an object is moving and the time it has been moving at that speed.

Here's how you can use this formula to solve various problems involving speed, time, and distance:

  1. Given Speed and Time, Find Distance: If you know the speed at which an object is moving and the time it has been moving at that speed, you can find the distance traveled by multiplying the speed by the time.

    Distance = Speed × Time

  2. Given Distance and Time, Find Speed: If you know the distance traveled by an object and the time it took to travel that distance, you can find the speed at which it was moving by dividing the distance by the time.

    Speed = Distance / Time

  3. Given Distance and Speed, Find Time: If you know the distance traveled by an object and the speed at which it was moving, you can find the time it took to travel that distance by dividing the distance by the speed.

    Time = Distance / Speed

These formulas are applicable in various real-life scenarios, such as calculating travel times, estimating speeds of moving objects, or determining distances covered during specific time intervals.

Varun and Arun start from a fixed point. Varun moves 3 km north and turns right and then covers 4 km. Arun moves 5 km west and turns right and walks 3 km - FAQs

1. What is the initial position of Varun and Arun?

Both Varun and Arun start from the same fixed point, assumed to be the origin (0,0).

2. What direction does Varun move initially?

Varun moves 3 km north from the starting point.

3. What direction does Arun move initially?

Arun moves 5 km west from the starting point.

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