Ratio and proportion

Anne completes a circuit around a circular track in 40 seconds. Brenda runs in the opposite direction and meets Anne every 15 seconds. How long does it take Brenda to run around the track?

Weekly Problem 37 - 2007
This regular hexagon has been divided into four trapezia and one hexagon.... what is the ratio of the lengths of sides p, q and r?

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.

A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone will the liquid rise?

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?

Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. What is the value of r/R?

The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?

A male punky fish has 9 stripes and a female punky fish has 8 stripes. I count 86 stripes on the fish in my tank. What is the ratio of male fish to female fish?

Can you fill in the mixed up numbers in this dilution calculation?