Question : A train travelling from Mumbai to Goa covered the first 420 km at a speed of 60 km\hr and then covered the remaining 95 km at a speed of 65 km/hr. Find its average speed in km/hr.
Option 1: 63.5
Option 2: 60.86
Option 3: 62
Option 4: 62.3
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Correct Answer: 60.86
Solution :
Distance travelled at the speed of 60 km/hr = 420 km
Time taken to travel 420 km at the speed of 60 km/hr = $\frac{420}{60}$= 7 hour
Distance travelled at the speed of 65 km/hr = 95 km
Time taken to travel 95 km at the speed of 65 km/hr = $\frac{95}{65}= \frac{19}{13}$ hour
We know: Average Speed = $\frac{\text{Total distance}}{\text{Total time}}$
Average Speed = $\frac{420 + 95}{7+\frac{19}{13}}$
= $\frac{515\times 13}{110}$
= $60.86$ km/hr
Hence, the correct answer is 60.86.
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