Question

A man travelled two fifths of his journey by train, one-third by bus, one-fourth by car and the remaining \[3\] km on foot. What is the total length of his journey?

Answer 1

Hint: At first, we will find the total length of the journey that he already covered. Then from the remaining part we will find the actual length of it. That is by assigning a variable to the total length we will find the required answer.

Complete step-by-step answer: It is given that a man travelled two fifth of his journey by train, one-third by bus, one-fourth by car and the remaining \[3\] km on foot.
We have to find the length of his journey.
Let us consider the total length of the journey as \[x\] km.
He travelled two fifths of his journey by train.
That is the distance he covered by train \[ = \dfrac{{2x}}{5}\]
He travelled one-third of his journey by bus.
That is the distance he covered by train \[ = \dfrac{x}{3}\]
He travelled one-fourth by car.
So, the distance he covered by car \[ = \dfrac{x}{4}\]
So, the total distance he covered by train, bus and car is \[ = \dfrac{{2x}}{5} + \dfrac{x}{3} + \dfrac{x}{4}\]
By simplifying we get,
The total distance he covered by train, bus and car is \[ = \dfrac{{59x}}{{60}}\]
The length of the remaining journey is \[ = x - \dfrac{{59x}}{{60}} = \dfrac{x}{{60}}\]
It is given that the remaining distance he travelled is \[3\] km on foot.
As per the problem,
On equating the remaining distance we get,
\[\dfrac{x}{{60}} = 3\]
On multiplying both sides by 60 we get,
\[x = 180\]
Hence, the length of the total journey is \[180\] km.

Note: Since, we have fraction length of the travel we can take the length of the total journey as \[1\]. Hence by adding the final fraction of walk with the total fraction found by adding fraction of bus, train and car we get 1.