$13$ $\newline$ Naomi travels to an interview. $\newline$ She travels by car for $\frac{1}{3}$ of the journey. $\newline$ She travels by train for $\frac{5}{8}$ of the journey. $\newline$ She walks for the remaining $500 \mathrm{~m}$ of the journey. $\newline$ Find the length of this journey in kilometres.

Full solution

13

\newline

Naomi travels to an interview.

\newline

She travels by car for

\frac{1}{3}

of the journey.

\newline

She travels by train for

\frac{5}{8}

of the journey.

\newline

She walks for the remaining

500 \mathrm{~m}

of the journey.

\newline

Find the length of this journey in kilometres.

Calculate fraction not covered: Calculate the fraction of the journey that is not covered by car or train. $\newline$ $1 - \frac{1}{3} - \frac{5}{8} = \frac{24}{24} - \frac{8}{24} - \frac{15}{24} = \frac{24 - 8 - 15}{24} = \frac{1}{24}$ .
Convert remaining distance: Convert the remaining distance from meters to kilometers. $\newline$ $500\,\text{m} = 0.5\,\text{km}$ .
Find total journey: Since $\frac{1}{24}$ of the journey is $0.5\,\text{km}$ , multiply by $24$ to find the total journey. $\newline$ $0.5\,\text{km} \times 24 = 12\,\text{km}.$