A man covers half part of a certain distance at 25 km/ hr. He covers 40 percent of remaining distance at the speed of 8 km/hr and covers rest of the distance at the speed of 18 km/hr. What is his average speed for the entire journey.

\(\frac{600}{37}\) km/hr

Let total distance be 100 km

50% of 100 km = 50 km @ 25 km/hr         ............(i)

Remaining distance = 100 - 50 = 50 km    

40% of rem.50 km = 20 km @ 8 km/hr      ...........(ii)

Remaining distance = 100 - (50 + 20) = 30km @ 18 km/hr   ...........(iii)

Time to cover the above distances:

(i) Time = \(\frac{50}{25}\) = 2 hrs

(ii) Time = \(\frac{20}{8}\) = \(\frac{5}{2}\) hrs

(iii) Time = \(\frac{30}{18}\) = \(\frac{5}{3}\) hrs

Total time = 2 + \(\frac{5}{2}\) + \(\frac{5}{3}\) hrs = \(\frac{37}{6}\)  hrs

⇒ Average speed = \(\frac{Total\;distance}{ Total\;time}\)

                          =  \(\frac{100}{\frac{37}{6}}\)

                          = \(\frac{600}{37}\) km/hr