Question : If a person travels a certain distance at a speed of 10 km/h and returns through the same route at a speed of 20 km/h, then what will be the average speed during the whole journey?
Option 1: $\frac{40}{3}$ km/h
Option 2: 15 km/h
Option 3: $\frac{10}{3}$ km/h
Option 4: $\frac{20}{3}$ km/h
Correct Answer: $\frac{40}{3}$ km/h
Solution :
Average Speed = $\frac{\text{Total Distance}}{\text{Total Time}}$
Let the distance be $D$ from either side (in kilometres).
For the forward journey at 10 km/h, the time taken is $\frac{D}{10}$hours.
For the return journey at 20 km/h, The time taken is $\frac{D}{20}$ hours.
The total time = $\frac{D}{10}+\frac{D}{20}$
So, average Speed = $\frac{\text{2D}}{\text{$\frac{D}{10}$+$\frac{D}{20}$}}$
= $\frac{\text{2D}}{\text{$\frac{2D}{20}$+$\frac{D}{20}$}}$
= $\frac{\text{2D}}{\text{$\frac{3D}{20}$}}=\frac{40}{3}$
⇒ average Speed = $\frac{40}{3}$ km/h
Hence, the correct answer is $\frac{40}{3}$ km/h.
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