The speed of the train going from Nagpur to Allahabad is 100 km/h while when coming back from Allahabad to Nagpur, its speed is 150 km/h. find the average speed during whole journey.

  • 125 km/hr
  • 75 km/hr
  • 135 km/hr
  • 120 km/hr

To find the average speed for the whole journey, you can use the formula for average speed:

Average Speed=Total DistanceTotal Time

Let’s assume the one-way distance between Nagpur and Allahabad is D. The total distance for the round trip is 2D, as the train is traveling from Nagpur to Allahabad and then back from Allahabad to Nagpur.

Let t1 be the time taken to travel from Nagpur to Allahabad, and t2 be the time taken to travel back from Allahabad to Nagpur.

The average speed is given by:

Average Speed=2Dt1+t2

To find t1 and t2, you can use the formula time=distancespeed

For the journey from Nagpur to Allahabad: t1=D100

For the journey back from Allahabad to Nagpur: t2=D150

Now, substitute these values into the average speed formula:

Average Speed=2DD100+D150

To simplify, you can find a common denominator and then cancel out terms:

Average Speed=2D3D+2D300

Average Speed=2D5D300

Average Speed=2D×3005D

Average Speed=6005

Average Speed=120km/h

So, the average speed during the whole journey is 120 km/h.

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