Water is flowing from a major broken water main at the intersection of two streets. The resulting puddle of water is circular and the radius r of the puddle is given by the equation r = 5t feet, where t represents time in seconds elapsed since the the main broke.

Question

(a) When the main broke, a runner was located 6 miles from the intersection. The runner continues toward the intersec- tion at the constant speed of 17 feet per second. When will the runner’s feet get wet?
(b) Suppose, instead, that when the main broke, the runner was 6 miles east, and 5000 feet north of the intersection. The runner runs due west at 17 feet per sec- ond. When will the runner’s feet get wet?

Answer 1

(a) when 5t + 17t = 6*5280
(b) when 5t = √(5000^2+(6*5280-17t)^2)