*Challenge question #31 (04/10/2016)*

**Junior Question**

Water can be supplied to a tank through either or both of two pipes. Using the smaller pipe alone, the tank takes two hours longer to fill than if the larger pipe is used alone. Using both pipes, the tank is filled in $1\frac{7}{8}$ hours.

How long does it take to fill the tank using only the larger pipe?

**Senior Question**

All six faces of a polyhedron are cyclic quadrilaterals. Show that the vertices lie on a sphere.