Question

car travels at speed X m/s from A to B, and returns From B to A at speed of Y m/s , find average speed of car
2 points

Answer 1

Answer:

• Average speed of the car is 2XY/(Y + X) m/s.

Step-by-step explanation:

Given that:

• A car travels at speed X m/s from A to B.
• And returns from B to A at speed of Y m/s.

To Find:

• Average speed of the car.

Let us assume:

• The distance from A to B be Z.

We know that:

• Distance = Speed × Time
• Time = Distance/Speed
• Speed = Distance/Time
• Average speed = Total distance/Total time

Finding the time to cover distance from A to B:

• Time = Distance/Speed
• Time = Z/X

Finding the time to cover distance from B to A:

• Time = Distance/Speed
• Time = Z/Y

Finding the total time taken:

• A to B = Z/X
• B to A = Z/Y

• Total time = Z/X + Z/Y
• Total time = Z(1/X + 1/Y)
• Total time = Z(Y + X)/XY

Finding the total distance:

• A to B = Z
• B to A = Z

• Total distance = 2Z

Finding the average speed of car:

• Average speed = Total distance/Total time

We have.

• Total distance = 2Z
• Total time = Z{Y + X)/XY

• Average speed = 2Z/{Z(Y + Z)/XY}
• Average speed = (2Z × XY)/{Z(Y + X)}
• Average speed = 2XY/(Y + X)

Hence,

• Average speed of the car = 2XY/(Y + X) m/s

Answer 2

Given :-

Car  travels at speed X m/s from A to B, and returns From B to A at speed of Y m/s ,

To Find :-

Average speed

Solution :-

Let the distance be d

We know that

Time = Distance/Speed

Time = d/x

When B to A

Time = d/y

Now,

The total time taken by A and B

d/x + d/y

Taking d as common

d(1/x + 1/y)

d(1 + 1/xy)

d(y + x/xy)

Now

The total distance covered by A and B

Total Distance = d + d

Total Distance = 2d

Avg. Speed = 2d/d(x + y)/xy

Avg. speed = 2d(xy)/d(y + x)

Avg. Speed = 2xy/y + x