A and B started their journeys from X to Y and Y to X, respectively.  After crossing each other, A and B completed their remaining journey in 6\(\frac{1}{8}\) and 8 h respectively.  If speed of A is 32 km/h, find the speed of B (km/h).

28

Let meeting time = t hours,

speed of A = S₁ and speed of B = S₂

time taken by A after meeting = t₁

time taken by B after meeting = t₂,

ATQ,

t₁ = 6\(\frac{1}{8}\) = \(\frac{49}{8}\)

t₂ = 8

\(\frac{S_1}{S_2}\) = \(\sqrt {\frac{t_2}{t_1}}\)

\(\frac{32}{S_2}\) = \(\sqrt {\frac{\frac{49}{8}}{8}}\)

\(\frac{32}{S_2}\) = \(\sqrt {\frac{64}{49}}\)

\(\frac{32}{S_2}\) = \(\frac{8}{7}\)

S₂  = 7 × 4 = 28