Question : Ramesh, on his way to his hometown, travelled the first 250 km at a speed of 75 km/hr and the next 250 km at a speed of 85 km/hr. Find the average speed for the whole journey (correct to 2 decimal places).
Option 1: 80.55 km/hr
Option 2: 79.69 km/hr
Option 3: 79.20 km/hr
Option 4: 80.69 km/hr
Correct Answer: 79.69 km/hr
Solution :
Given: Ramesh travelled the first $250$ km at $75$ km/hr.
So, the time taken was $\frac{250}{75}=\frac{10}{3}$ hr
The next $250$ km were covered at the speed of $85$ km/hr.
So, the time taken was $\frac{250}{85}=\frac{50}{17}$ hr
Average speed for the whole journey
$=\frac{\text{Total distance}}{\text{Total time taken on journey}}$
$=\frac{250+250}{\frac{10}{3} + \frac{50}{17} }$
$=500×\frac{51}{320}$
$=79.69$ km/hr
Hence, the correct answer is 79.69 km/hr.
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