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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.
Answer & Solution
Correct Answer:
Option
D
$$\eqalign{
& {\text{Average speed}}, \cr
& = \frac{{ {2 \times x \times y} }}{{ {x + y} }} \cr
& = \frac{{ {2 \times 100 \times 150} }}{{ {100 + 150} }} \cr
& = \frac{{ {200 \times 150} }}{{250}} \cr
& = 120\,{\text{km/hr}} \cr} $$
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LoginLet 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.
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
(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❣️❣️
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
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.
B+A=150
(100+150) /2= 120
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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