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.

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So the formula of average speed with same distance can be broken as such:
Let the distance be S
So the average speed = total distance covered/total time taken
= 2S / [ (S/100) + (S/150) ]
Carefully Solve this Equation You will get 120 km/hr ANS.

amazing

Let, the distance is=s
the first speed is =x
the 2nd speed is=y
So, the time to cover s distance in x speed is
t₁= s/x
Hence, t₂= s/y
Now, we know,
average speed= total distance/total time
=(s+s)/(s/x+s/y)
= 2s/ s(1/x+1/y) [taking s common]
=2/ (1/x+1/y) [ s is cancelled out]
=2/ (x+y/xy) [fraction add rule]
= 2xy/x+y
This is how the formula came.



the 2nd speed is =y
So, total distance is, s+s=2s

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Why we not explain using
(100+150)/2 =250/2 = 125
Because for average we add the values of terms and the divide it by the number of terms.......or is it fault mathod????please guide sir❣️❣️

Average speed m 2 se kyu multiply kia...

Let me give you a clear Explaination:
What is formula for speed? ( speed= dist/time ) right!.
So in the same way average speed=(Total dist/Total time).
let -> dist=z speed1=x speed2=y now speed=(z+z)/(time1+time2)
====>now, Total Dist= z+z(becoz two way journey) =2z , (time =dist/speed) so time1=(z/x), time2=(z/y)
====>avg speed= (2z) / z *((1/x)+(1/y)) (z was taken common from both)
====>avg speed = 2 / ((1/x)+(1/y))
finally avg speed= 2*x*y / (x+y)
This is derivation of formula. Keep smiling

Why we can't solve it by 100+15/2=125

Why we can't solve it by 100+15/2=125

nice

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 and again going to the same way Nagpur to Allahabad at a speed of 120km/hr.Find the average speed during whole journey...

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.

Yes

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

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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

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

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

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

Why we should multiply 2 before it?

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.

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