Question

A man travelled $\frac{3}{5}$ of his journey by rail, $\frac{1}{4}$ by a taxi, $\frac{1}{8}$ by a bus, and the remaining $2$ km on foot. What is the length of his total journey?

Answer 1

Let the length of the total journey be $x$ km.

According to the question, we have:

$\frac{3}{5}x+\frac{1}{4}x+\frac{1}{8}x+2=x$

$\Rightarrow \frac{3\times 8}{5\times 8}x+\frac{1\times 10}{4\times 10}x+\frac{1\times 5}{8\times 5}x+\frac{2\times 40}{1\times 40}=x$

$\Rightarrow \frac{24x}{40}+\frac{10x}{40}+\frac{5x}{40}+\frac{80}{40}=x$

$\Rightarrow \frac{24x+10x+5x+80}{40}=x$

$\Rightarrow 39x+80=40x$

$\Rightarrow x=80$

$\therefore$ The length of his total journey is $80$ km.