Nella travelled 1/3 of a journey by bus, 2/3 of the remainder by bicycle and the remaining 9km on foot. (a) how far did nella cycle (b) what was the total distance travel
+26400 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
\(\begin{array}{rcll} b &=& \frac13 \cdot j \\ b &=& \frac13 \cdot 40.5\ \text{km} \\ b &=& 13.5\ \text{km} \\ \end{array}\)
