Question

Two aeroplanes start from the same place in opp directions. One goes towards cast at \(320 \mathrm{~km} / \mathrm{h}\) and the other goes towards west at \(400 \mathrm{~km} / \mathrm{h}\) what time will they take to be \(720 \mathrm{~km}\) apart? (a) \(4 \mathrm{~h}\) (b) \(3 \mathrm{~h}\) (c) \(1 \mathrm{~h}\) (d) \(1.5 \mathrm{~h}\)

Short answer

Answer: (c) 1 h

Step-by-step solution

Determine the combined speed of the airplanes

Since the airplanes are flying in opposite directions, their speeds can be combined to find the rate at which they are moving apart. The combined speed is the sum of their individual speeds: Combined speed = Speed of plane towards east + Speed of plane towards west = 320 km/h + 400 km/h = 720 km/h

Use the distance formula to find the time

To find the time it takes for them to be 720 km apart, we can use the formula for distance: distance = speed × time Rearrange the formula to solve for time: time = distance / speed Substitute the values: time = 720 km / 720 km/h

Calculate the time and find the answer

Now, we can calculate the time: time = 720 km / 720 km/h = 1 h So, they will take 1 hour to be 720 km apart. The correct answer is: (c) 1 h

Key concepts

Distance and Speed Formula

Understanding the relationship between distance, speed, and time is essential when solving motion problems. One common formula used is the distance formula:

• Distance = Speed × Time

This formula allows you to calculate the distance traveled by an object when you know its speed and the time it has been traveling.
In the exercise, two airplanes travel in opposite directions with their speeds given as 320 km/h and 400 km/h. The combined speed becomes crucial since the planes are moving away from each other, effectively increasing the rate at which they distance themselves. Adding these speeds gives us a combined speed of 720 km/h. This represents the distance both planes cover together every hour.
The simple rearrangement of the formula to

• Time = Distance / Speed

is used in calculations after determining the combined speed.

Time Calculation

Calculating the time taken for two objects moving in opposite directions requires knowing their rates. Since the airplanes have a combined speed of 720 km/h and need to be 720 km apart, we apply the time calculation formula.
With

• Distance = 720 km (total distance they need to be apart)
• Combined speed = 720 km/h

Using

• Time = Distance / Speed

we plug the values:

• Time = 720 km / 720 km/h

This simplifies to:

• Time = 1 hour

This calculation shows it takes only 1 hour for the planes to be 720 km apart.

Motion in Opposite Directions

When two objects move in opposite directions, their speeds add up because they are moving away from each other. This composite speed is crucial in problems requiring knowledge of how quickly two objects separate.
In this scenario, the airplanes move at 320 km/h and 400 km/h. Since they start from the same point, their separation is the sum of their speeds.
So, their relative speed, when moving in opposite directions, is:

• 320 km/h + 400 km/h = 720 km/h

Knowing this helps understand how quickly two entities at given speeds can distance from each other. Contextualizing this in real-life, imagine two friends walking in opposite directions: the more they both walk faster, the quicker they are miles apart. This principle is used repeatedly in various motion problems, and mastering it can make solving such problems straightforward and intuitive.