Science:Math Exam Resources/Courses/MATH101/April 2005/Question 05 (b)/Statement

A water tank with depth 3 feet is in the shape of the trough depicted below. The bottom edge of the tank is 1 foot above the ground, and the ends of the tank are equilateral triangles of side length $2{\sqrt {3}}$ feet; the top of the tank is a rectangle of length 12 feet and width $2{\sqrt {3}}$ feet.

(b) Sometime after it is filled, the tank develops a small hole at its bottom. The tank then drains according to Toricelli's Law:

$A(y){\frac {dy}{dt}}=-k{\sqrt {y}},$

where $y$ is the height of the water in the tank above its bottom, $A(y)$ is the area of the horizontal cross-section of the tank at height $y$, and $k$ is a positive constant. If the water level in the tank drops to 1 foot after 2 hours, how long will it take for the tank to empty?

(Do not simplify you answer.)