A travels a certain distance with three different speeds; first 3 km with a speed of 9 km/h, second 6 km with a speed of 15 km/h, and third 9 km with a speed of 18 km/h. What is the average speed of A for the whole journey?

A travels a certain distance with three different speeds S1, S2, S3 three different times T1, T2, T3 and covers different distance D1, D2, D3

Average speed = $$\frac{Total\ distance}{Total\ time}$$

T1 = $$ \frac{3}{9} = \frac{1}{3} $$

T2 = $$ \frac{6}{15} = \frac{2}{5} $$

T1 = $$ \frac{9}{18} = \frac{1}{2} $$

Total time = T1 + T2 + T3 = $$ \frac{37}{30} $$

Total distance = D1 + D2 +D3 = 3 + 6 + 9 = 18

Substituting,

Average speed = $$ \frac{18}{\frac{37}{30}} $$

                      = $$ \frac{540}{37} $$