Question

The speed of the train in going from Nagpur to Pune is 105 km/hr. while when coming back from Pune to Nagpur its speed is 70 km/hr. Find the average speed during the whole journey.​

Answer 1

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$\tt{nagpur \: to \: pune \: ,u = 105 \: km/hr} \\ \\\tt{ pune \: to \: nagpur \: ,v = 70 \: km/hr} \\ \\ \tt{average \: speed} = \tt \frac{2uv}{u + v} \\ \\ = \tt\frac{2 \times 105 \times 70}{105 + 70} \\ \\ = \tt\frac{14700}{175} \\ \\ =\tt\large \color{lime}\underline{\underline{84 \: km/hr}}$

Answer 2

Answer:

84 km/hr

Step-by-step explanation:

Let the distance between Nagpur & Pune be x km

Therefore on a return journey total distance covered = x + x = 2x

Now time taken from Nagpur to Pune = $\frac{x}{105} Hours$

(As Time  = Distance/Speed)

And similarly from Pune to Nagpur = $\frac{x}{70} Hours$

Total time taken = $\frac{x}{105} + \frac{x}{70} = \frac{x}{42} Hours$

Average Speed = Total Distance Covered/Total Time Taken = $\frac{2x}{\frac{x}{42} }$   =  84

Therefore Average Speed = 84 Km/Hr