A train runs at a speed of 137 kmph to cover a distance of 411 km and then at a speed of 109 kmph to cover a distance of 327 km. Find the average speed of the train for the entire distance.

Correct option is A

Given:

The train runs at a speed of 137 km/h to cover a distance of 411 km.

The train then runs at a speed of 109 km/h to cover a distance of 327 km.

Concept Used:

The average speed for the entire journey is given by the formula:

Average speed = $$\frac{\text{Total distance}}{\text{Total time}}$$​​

Where:

Total distance = Distance covered at the first speed + Distance covered at the second speed.

Total time = Time taken to cover the first distance + Time taken to cover the second distance.

The time to cover a distance is given by:

Time = $$\frac{\text{Distance}}{\text{Speed}}$$​​

Solution:

Total distance covered by the train:

Total distance = 411 + 327 = 738 km

Time taken to cover the first part of the journey:

Time1 = $$\frac{411}{137}$$​= 3 hours

Time taken to cover the second part of the journey:

Time2 = $$\frac{327}{109}$$​ = 3 hours

Total time = 3 + 3 = 6 hours

Now,

Average speed = $$\frac{738}{6}$$​ = 123 km/h

Thus, the average speed of the train for the entire distance is 123 km/h.