math fraction question

Nella travelled 1/3 of a journey by bus, 2/3 of the remainder by bicycle and the remaining 9km on foot.

j = journey

c = cycle

b = bus

(a) how far did nella cycle

$\begin{array}{lrcll} (1) & c &=& (\frac23\cdot j) \cdot \frac23 \\ & \frac23\cdot j &=& \frac32\cdot c \\\\ (2) & c + 9\ \text{km} &=& \frac23 \cdot j \\ & c + 9\ \text{km} &=& \frac32\cdot c \\ & \frac32\cdot c - c &=& 9 \\ & \frac12\cdot c &=& 9 \\ & c &=& 18\ \text{km}\\ \end{array}$

Nella cycle 18 km

(b) what was the total distance travel

$\begin{array}{lrcll} & \frac23\cdot j &=& \frac32\cdot c \\ & j &=& \frac32\cdot \frac32\cdot c \\ & j &=& \frac32\cdot \frac32\cdot 18\ \text{km} \\ & j &=& 40.5\ \text{km} \end{array}$

The total distance travel was 40.5 km

$\begin{array}{rcll} b &=& \frac13 \cdot j \\ b &=& \frac13 \cdot 40.5\ \text{km} \\ b &=& 13.5\ \text{km} \\ \end{array}$

Let the total distance be =D

1/3D.2/3D =9

2/9D=9

D=9.9/2

D=40.5 Km. Total diseance

40.5 1/3=13.5 Km by bus

27.2/3 =18 Km by cycle

9 Km by foot.