# 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.

A. 125 km/hr

B. 75 km/hr

C. 135 km/hr

D. 120 km/hr

### Solution(By Examveda Team)

\eqalign{ & {\text{Average speed}}, \cr & = \frac{{ {2 \times x \times y} }}{{ {x + y} }} \cr & = \frac{{ {2 \times 100 \times 150} }}{{ {100 + 150} }} \cr & = \frac{{ {200 \times 150} }}{{250}} \cr & = 120\,{\text{km/hr}} \cr}

1. Average Speed = 2ab/(a + b)

Applicable when one travels at speed a for half the distance and speed b for other half of the distance. In this case, average speed is the harmonic mean of the two speeds. On similar lines, you can modify this formula for one-third distance.

2. Yes

3. A+B=100
B+A=150
(100+150) /2= 120

4. Dear Sir,
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5. So the formula of average speed with same distance can be broken as such:
Let the distance be n
So the average speed = total distance covered/total time taken
= 2n/[(n/100)+(n/150)]
= 2n/[(n/x)+(n/y)]
= 2n[(nx+ny)/xy]
= 2n[n(x+y)/xy]
= 2(x+y)/xy

6. Can you please point me to some article which would help understanding this formulae for finding the average speed . Or some different formula for calculating train speed average

7. Let the distance between them is 300 km,so total distance covered is 600 km...from Nagpur to Allahabad speed is 100 kmph so time taken is 3 hrs. And while retiring it's speed is 150kmph so time taken is 2 hrs...so total distance is 600 km nd total time taken is 5 hrs and by applying the basic formula we will get 120 kmph

8. Its is the formula of the finding average speed of two variant of speed for the same distance. where 'x' and 'y' are the speed of the train receptively

9. Why we should multiply 2 before it?

10. Its is the formula of the finding average speed of two variant of speed for the same distance. where 'x' is the speed of the train towards Nagpur to Allahabad and 'y' s the speed of the train moving towards Allahabad to Nagpur.

11. (2*x*y)/(x+y) what is this

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