A starts walking at 4 k mph and after 4 hours, B starts cycling from the same point as that of A, in the same direction at 10 k mph. After how much distance from the starting point will B catch up with A (Correct to two decimal places)?

As per the given question,

Distance covered by man in 4 hour $$=4\times4=16$$km

Let cyclist and walking person will meet after time t and at the distance d from the starting point.

Hence, for cyclist $$t=\dfrac{d}{10}$$--------(i)

For the walking person, $$t=\dfrac{d-16}{4}$$----------(ii)

From the equation (i) and (ii)

$$\Rightarrow \dfrac{d}{10}=\dfrac{d-16}{4}$$

$$\Rightarrow 4d=10d-16\times10$$

$$\Rightarrow 10d-4d=16\times10$$

$$\Rightarrow 6d=16\times10$$

$$\Rightarrow d=\dfrac{16\times10}{6}=26.67KM$$