Question : A person covers a certain distance by bus at 45 km/hr and immediately returns to the starting point by car at a speed of 80 km/hr. What is his average speed during the whole journey?
Option 1: 57.6 km/hr
Option 2: 63.2 km/hr
Option 3: 73.5 km/hr
Option 4: 45.5 km/hr
Correct Answer: 57.6 km/hr
Solution :
Let the total distance travelled by the person during the whole journey be $2x$ km.
We know, time = $\frac{\text{Total distance}}{\text{Total time}}$
So, time taken by him to travel $x$ km at a speed of 45 km/hr = $\frac{x}{45}$
Time taken by him to travel $x$ km at a speed of 80 km/hr = $\frac{x}{80}$
Total time taken by him during the whole journey = $\frac{x}{45} + \frac{x}{80}$ = $\frac{125x}{3600}$
Now, Average speed = $\frac{\text{Total distance}}{\text{Total time}}=\frac{2x}{\frac{125x}{3600}}=\frac{7200}{125}= 57.6$ km/hr
Hence, the correct answer is 57.6 km/hr.
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