Question : R jogs at twice the speed of walking and runs at twice the speed of jogging. From his home to office, he covers half of the distance by walking and the rest by jogging. From his office to home, he covers half the distance jogging and the rest by running. What is his average speed (in km/hr) in a complete round from his home to office and back home if the distance between his office and home is 10 km and he walks at the speed of 5 km/hr?
Option 1: $\frac{90}{8}$
Option 2: $\frac{60}{8}$
Option 3: $\frac{60}{9}$
Option 4: $\frac{80}{9}$
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Correct Answer: $\frac{80}{9}$
Solution :
R's jogging speed = 5 × 2 = 10 km/hr
R's running speed = 10 × 2 = 20 km/hr
Now,
At the time of going to his office time taken $= \frac{5}{5} + \frac{5}{10} =1 + 0.5 = 1.5$ hours
At the time of returning to his home time taken $= \frac{5}{10} + \frac{5}{20}= 0.5 + 0.25= 0.75$ hour
Total time = 1.5 + 0.75 = 2.25 hours or $\frac{9}{4}$ hours
Total distance covered by R = 20 km
So, the average speed $= \frac{20}{\frac{9}{4}}=\frac{20\times 4}{9}=\frac{80}{9}$ km/hr
Hence, the correct answer is $\frac{80}{9}$.
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