Question : A man covers a total distance of 100 kilometres on a bicycle. For the first 2 hours, the speed was 20 km/hr and for the rest of the journey, it came down to 10 km/hr. The average speed will be:
Option 1: $12\frac{1}{2}\ \text{km/hr}$
Option 2: $13\ \text{km/hr}$
Option 3: $15\frac{1}{8}\ \text{km/hr}$
Option 4: $20\ \text{km/hr}$
Correct Answer: $12\frac{1}{2}\ \text{km/hr}$
Solution :
Given:
Total distance = 100 km
The distance covered in the first 2 hours at 20 km/hr:
Distance = Speed × Time = 20 × 2 = 40 km
Distance left to cover is (100 – 40) = 60 km
Time taken to cover the remaining 60 km at a speed of 10 km/hr:
Time for the rest of the journey = $\frac{\text{Distance}}{\text{Speed}}=\frac{60}{10}$ = 6 hours
Total time taken = 2 hours + 6 hours = 8 hours
Average speed = $\frac{\text{Total distance}}{\text{Total time}}=\frac{100}{8}=12\frac{1}{2}\ \text{km/hr}$
Hence, the correct answer is $12\frac{1}{2}\ \text{km/hr}$.
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