Question 31

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?

Answer

It would take $3$ hours to fill the tank using only the larger pipe.

Worked Solution

Senior Question

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

Hint

Given any $4$ non-coplanar points, there is a unique sphere passing through these points.

Worked Solution