2015 UNCO Math Contest II Problems/Problem 4

Problem

Tarantulas and start together at the same time and race straight along a foot path, each running at a constant speed the whole distance. When reaches the end, still has feet more to run. When reaches the end, has feet more to run. How many more feet does Tarantula have to run when Tarantula reaches the end?

Solution

Convert the speeds to fractions that relate between the various speeds. Tarantula A runs feet in the time Tarantula B runs feet, which implies that Tarantula B's speed is th of Tarantula A's speed. Similarly, Tarantula C's speed is or th of Tarantula B's speed. Multiplying by yields . Multiplying this by feet (the total distance), we find that when Tarantula A finishes, Tarantula C is feet in, so Tarantula C has feet left when Tarantula A finishes.