Question

A man completes $${\displaystyle \frac{6}{11}}$$ of a 231 km journey by train, $${\displaystyle \frac{3}{7}}$$ by bus and the rest on foot. What distance did the man walk?

Answer 1

Hint: Determine the distance the man covered by train and then by bus and subtract from the total distance to obtain the distance he covered by walk.

Complete step-by-step answer:
It is given that the man completes $${\displaystyle \frac{6}{11}}$$ of a 231 km journey by train.
We know that the distance the man covered by train is the product of the fraction of the distance covered by the train and the total distance. Hence, we have:
Distance covered by man by train = $${\displaystyle \frac{6}{11}}\times 231km$$
Distance covered by man by train = $$6\times 21km$$

Distance covered by man by train = $$126km...........(1)$$

Therefore, the man covered 126km by train.
It is given that the man completes $${\displaystyle \frac{3}{7}}$$ of the 231 km journey by bus.
We know that the distance the man covered by bus is the product of the fraction of the distance covered by the bus and the total distance. Hence, we have:
Distance covered by man by bus = $${\displaystyle \frac{3}{7}}\times 231km$$
Distance covered by man by bus = $$3\times 33km$$

Distance covered by man by bus = $$99km...............(2)$$
The distance the man covered by walking is the difference between the total distance he covered and the sum of the distances he covered by train and bus. Then, from equation (1) and equation (2), we have:
Distance covered by man by walk = $$231-126-99$$
Distance covered by man by walk = $$6km$$
Hence, the man covered 6 km by walk.

Note: We can also find the fraction he walked by subtracting the sum of the fractions he covered by train and bus from 1. Then, we can multiply with the total distance to find the distance he covered by walk.