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 main broke.
When the main broke, A runner was 6 miles east and 5000 feet north of the intersection. The runner is due west at 17 feet per second. When will the runner's feet get wet?
The Attempt at a Solution
Not exactly sure how to solve this problem but here's all I got:
- Triangle, on the x-axis labelled it 31, 680 ft, on the y-axis labelled it 5,000 ft. The hypotenuse is then 32, 072.1437 ft.
- Diffierientiated x^2 + y^2 = r^2 and got 2x dx/dt + 2y dy/dt = 2 r dr/dt
- Looked back at the equation r = 5t, found r' to be 5, so dr/dt =5
- Just pluged the 5 back in like any algebra problem and got
5,000dx/dt + 31,680(-17) = 5(32072.1437)
dx/dt = 139. 784144
Not sure where I went wrong, I plugged the equation back into r = 5t and got 27.95 -- the book says 25.4154041 minutes so there's something wrong here