Question

After travelling $\frac{2}{3}$of his journey ,Rajesh noticed that he had still to go $4\frac{1}{2}km$

(a) How long was his journey?

(b) What distance he has travelled?

Answer 1

Step 1 :- To find the total distance of journey

Let the total distance be $x$,

So after travelling $\frac{2}{3}$ part of journey, remaining part = $x-\frac{2x}{3}=\frac{(3-2)x}{3}=\frac{x}{3}$

But given that still he has to travel $4\frac{1}{2}km$,

i.e. $4\frac{1}{2}km=\frac{4\times 2+1}{2}km=\frac{9}{2}km$

Therefore,

$$\begin{gathered} \frac{x}{3}=\frac{9}{2} \\ 2\times x=9\times 3 \\ x=\frac{27}{2}=13\frac{1}{2}km \end{gathered}$$

Total distance of journey = $13\frac{1}{2}km$

Step 2 :- To find distance he has travelled

He has travelled $\frac{2}{3}$part of journey,

Distance he travelled = $\frac{2}{3}\times \frac{27}{2}=\frac{9}{1}=9Km$

Therefore ,he has travelled $9km$