A boy standing by the side of a railway track finds that an Up train crosses him in 8 seconds and a Down train of twice the length of that of the Up train crosses him in 20 seconds. How long (in seconds) will the two trains take to cross each other?

Let the length of up train be x metres therefore, length of down train be 2x metres

Speed of up train = $$\frac{x}{8}$$

Speed of down train = $$\frac{2x}{20}$$

Relative speed = $$\frac{x}{8} + \frac{2x}{20} = \frac{9x}{40}$$

Time taken to cross each other = $$\frac{Sum  of  the  lenght  of  the  both  trains}{Relative  speed}$$

                                              = $$3x\times\frac{40}{9x}=\frac{40}{3}$$