Question

A train travels between two stations x and y. While going from x to y, its average speed is 72 km per hour, and while coming back from y to x, its average speed is 63 km per hour. Find the average speed of the train during the whole journey.

Answer 1

Answer:

Average speed = Total distanceTotal time

Now, let the distance between X and Y be 'a' m. As the distance will not change during the journey from the two points. Therefore, total distance covered = 2a km.

Now let the total time taken for the journey be = t hr

So,

Avg Speed = 2at

We know that,

Speed = distancetime

Case 1, from X to Y

Time = distance/speed

t = x/72 hr

Case 2, from Y to X

Time = distance/speed

t = x/63 hr

Therefore, total time taken

= x72 + x63 =7x + 8x504= 15x504= 5x168

Now using equation 1,

Avg speed = = 2x5x168= 2x × 1685x= 67.2 Km/hr

Therefore, its average speed throughout the journey was 67.2 Km/

Answer 2

Given:-

• A train travels between two stations x and y.
• While going from x to y, its average speed is 72 km per hour, and while coming back from y to x, its average speed is 63 km per hour.

⠀

To find:-

• The average speed of the train during the whole journey.

⠀

Solution:-

Let,

• the average speed be 2a.

⠀

Here,

• Average speed = 2a/t

⠀

We know that,

⇛ Speed = distance/time

⠀

Firstly,

• From X to Y.

⠀

⇛ Time = distance/speed

⇛ Time = x/72 hr

⠀

Then,

• From Y to X.

⠀

⇛ Time = distance/speed

⇛ Time = x/63 hr

⠀

Therefore,

• Total time taken.

⠀

⇛ x/72 + x/63

⇛ 7x + 8x/504

⇛ 15x/504

⇛ 5x/168

⠀

Now,

⇛ Average speed = 2x/5x/168

⇛ 2x × 168/5x

⇛ 67.2 Km/hr

⠀

Hence,

• its average speed throughout the journey is 67.2 Km/h.