Question : Sriya with her family travelled from Bolpur to Suri by car at a speed of 40 km/h and returned to Bolpur at a speed of 50 km/h. The average speed for the whole journey is:
Option 1: $44\frac{4}{9}$ km/h
Option 2: $45$ km/h
Option 3: $45\frac{1}{2}$ km/h
Option 4: $44.78$ km/h
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Correct Answer: $44\frac{4}{9}$ km/h
Solution : Let denote the distance between Bolpur and Suri as $d$. The time taken to travel from Bolpur to Suri is $\frac{d}{40}$ hours and the time taken to travel back from Suri to Bolpur is $\frac{d}{50}$ hours. So, the total distance travelled is $2d$ (to Suri and back) and the total time taken is $\frac{d}{40}$ + $\frac{d}{50}$ hours. The average speed $v$ for the whole journey is $v = \frac{{\text{Total distance}}}{{\text{Total time}}} = \frac{{2d}}{{\frac{d}{40} + \frac{d}{50}}}$ ⇒ $v = \frac{{2}}{{\frac{1}{40} + \frac{1}{50}}} = \frac{400}{9} = 44\frac{4}{9}$ km/h Hence, the correct answer is $44\frac{4}{9}$ km/h.
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