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 $$={\displaystyle \frac{2x}{5}}$$
He travelled one-third of his journey by bus.
That is the distance he covered by train $$={\displaystyle \frac{x}{3}}$$
He travelled one-fourth by car.
So, the distance he covered by car $$={\displaystyle \frac{x}{4}}$$
So, the total distance he covered by train, bus and car is $$={\displaystyle \frac{2x}{5}}+{\displaystyle \frac{x}{3}}+{\displaystyle \frac{x}{4}}$$
By simplifying we get,
The total distance he covered by train, bus and car is $$={\displaystyle \frac{59x}{60}}$$
The length of the remaining journey is $$=x-{\displaystyle \frac{59x}{60}}={\displaystyle \frac{x}{60}}$$
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,
$${\displaystyle \frac{x}{60}}=3$$
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.