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 (in km/h) 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/h?

$\frac{80}{9}$

Distance from home to office = 10 km

Walking speed = 5km/h

Jogging speed = 10 km/h

Running speed = 20 km/h

From Home to Office ,

According to question:-

Time Taken = \(\frac{5}{5}\) + \(\frac{5}{10}\) = 1.5 hour

From Office to Home ,

Time taken = \(\frac{5}{10}\) + \(\frac{5}{20}\)  =  0.5 + 0.25 = 0.75 hour

Average speed = \(\frac{20}{2.25}\)

= \(\frac{80}{9}\) km/h