A and B are travelling towards each other from the points P and Q respectively. After crossing each other, A and B take $$6\frac{1}{8}$$ hours and 8 hours, respectively, to reach their destinations Q and P, respectively. If the speed Of B is 16.8 km/h, then the speed (in km/h) Of A is:

As per the question,

Let the speed of the A is v,let both meet at O after the t.

Speed of B is $$=16.8$$Km/hour  given that B will reach to the point P after 8 hour from the point O and A will reach to the point Q after $$6\times{1}{8}=\dfrac{49}{8}$$hour

So, $$d_1=v\times t$$------------(i)

$$\Rightarrow d_2=16.8\times t$$---------(ii)

Now as per the condition given in the question,

$$\Rightarrow d_1=16.8\times 8 $$km

and $$d_2=v\times \dfrac{49}{8}$$km

From the equation (i) and (ii)

$$\Rightarrow \dfrac{d_1}{d_2}=\dfrac{v\times t}{16.8\times 8}$$

Now, substituting the values of $$d_1$$ and $$d_2$$

$$\Rightarrow \dfrac{16.8\times 8}{v\times \dfrac{49}{8}}=\dfrac{v\times t}{16.8\times t}$$

$$\Rightarrow v^2=\dfrac{16.8\times 8\times16.8\times 8}{49}$$

$$\Rightarrow v=\sqrt{\dfrac{16.8\times 8\times16.8\times 8}{49}}$$

$$\Rightarrow v=19.2km/hour$$