\(\frac{2}{5}\)th of the journey is covered at a speed of 30 km/h, \(\frac{1}{4}\)th of the journey at a speed of 25 km/h and rest at 60 km/h.  What is an avg. speed for the whole journey?

34.28

                           \(\frac{2}{5}\)th     \(\frac{1}{4}\)th     Remaining

Distance ratio       8     :     5     :     7

Speed                  30    :    25    :     60                         (LCM of 30, 25, 60 = 300)

multiply distance ratio by 300 to easy calculation     

D → 8 × 300    :    5 × 300    :    7 × 300

S →     30        :        25        :    60

Avg. speed = \(\frac{20 × 300}{80 + 60 + 35}\) = \(\frac{6000}{175}\) = 34.28