Rahul travels three equal distances on his cycle with the speeds of 8 km/hr, 10 km/hr and 15 km/hr and takes a total time of 2 hours 27 minutes. The total distance (in km) covered by him is:
25.2 km
Let each of the three equal distances be d km. Time = distance ÷ speed for each part.
Total time = \(\frac{d}{8} + \frac{d}{10} + \frac{d}{15} = \frac{15d + 12d + 8d}{120} = \frac{35d}{120} = \frac{7d}{24}\) hours.
2 hours 27 minutes = \(2 + \frac{27}{60} = \frac{147}{60} = \frac{49}{20}\) hours.
\(\frac{7d}{24} = \frac{49}{20} \Rightarrow d = \frac{49 \times 24}{20 \times 7} = 8.4\) km.
Total distance = 3 × 8.4 = 25.2 km.
Hence, the answer is 25.2 km.
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