A and B started their journeys from X to Y and Y to X, respectively. After crossing each other, A and B completed the remaining parts of their journeys in $$6\frac{1}{8}$$ h and 8 h respectively. If the speed of B is 28 km/h, then the speed (in km/h) of A is:
By the formula,
Ratio of the speed = $$\sqrt{\ inverse\ \ ratio\ \ of\ \ the  time}$$
$$\frac{S_a}{S_b} = \sqrt{\frac{t_b}{t_a}}$$
$$S_b = 28 km/hr$$
$$t_a =Â 6\frac{1}{8} = \frac{49}{8}$$
$$t_b = 8$$
$$\Rightarrow \frac{S_a}{28} = \sqrt{\frac{8}{\frac{49}{8}}}$$
$$\Rightarrow \frac{S_a}{28} =Â \sqrt{\frac{64}{49}}$$
$$\Rightarrow \frac{S_a}{28} = \frac{8}{7}$$
$$S_a = 32 km/hr$$
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