Question

A man travelled $\frac{3}{4}$ of his journey by train, $\frac{1}{5}$ by taxi and the remaining $5km$ on foot. What is the distance of his total journey?

Answer 1

Let the total distance be $x$ km.
Part of the journey travelled by train $=\frac{3}{5}$ of $x=\frac{3x}{5}$km
Part of the journey travelled by taxi $=\frac{1}{4}$ of $x=\frac{x}{4}$ km
Part of the journey tracvelled by bus $\frac{1}{8}$ of $x=\frac{x}{8}$ km.
Total journey travelled by vehicles
$=\frac{3x}{5}+\frac{x}{4}+\frac{x}{8}$km
$=\frac{24x+10x+5x}{40}$km
$=\frac{39x}{40}$km
Remaining journey travelled on foot
$=x-\frac{39x}{40}$km
$=\frac{40x-39x}{40}$ km
$=\frac{x}{40}$km
According to the question $\frac{x}{40}=6$
$\Rightarrow$ $x=6\times 40$km
$=240$km
Hence the total distance is $240$km