A and B start moving towards each other from places X and Y respectively at the same time on the same day.  The speed of A is 25% more than that of B.  After meeting on the way, A and B take Z hours and 6\(\frac{1}{4}\) hours, respectively to reach their destination. What is the value of Z?

4 hours

              A    :    B

Speed    5    :    4              [25% =  \(\frac{1}{4}\)]

S_A = 5, S_B = 4

t_A = Z, t_B = \(\frac{25}{4}\)

Here the formula is :

\(\sqrt {\frac{t_A}{t_B}}\) = \(\frac{S_B}{S_A}\)

ATQ

⇒ \(\sqrt {\frac{Z}{\frac{25}{44}}}\) = \(\frac{4}{5}\)

⇒ \(\sqrt {\frac{4Z}{25}}\) = \(\frac{4}{5}\)

square both sides

\(\frac{4Z}{25}\) = \(\frac{16}{25}\)

⇒ Z = 4 hours