The reflection Pool near the Washington Monument is a rectangle with a length that is 50 ft more then 15 times its width.

Question

The depth of the pool is 1/50 of the width. Let w represent the width of the pool.

(a): Write polynomial expressions for the length and depth of the pool in terms of w. Then write a polynomial expression for the volume of the pool in terms of w.

(b): The depth of the pool if 3 feet What is the volume?

Answer 1

a)

 

 

The term "times" means to multiply.  The term "more than" means add.  The term "of" also means multiply.

 

width = w

length = 15w + 50

depth = (1 / 50)w  ---->  we can also say  w / 50

 

 

b)

 

The volume of a rectangle is length times width times depth.  So we just multiply the three polynomials from part (a) when w=3.

 

Volume = w(15w + 50)(w / 50)

 

Volume = 3(15(3) + 50)(3 / 50)

 

Volume = 3(45 + 50)(3 / 50)

 

Volume = 3(95)(3 / 50)

 

Volume = 17.10 ft³