# Need help with algebraic word problem

• Feb 11th 2010, 05:57 AM
mcruz65
Need help with algebraic word problem
Rain-Gutter Design:

An open rectangular gutter is made by turning up the sides of a piece of metal 20 in. wide. The area of the cross-section of the gutter is 50 in^2. Find the depth of the gutter.

So far this is what I have done:
A= LW
50 = L (20)
L = A/W = 50/20 = 2.5 in

Is this correct?
• Feb 11th 2010, 08:43 AM
bjhopper
rain gutter design
posted by mcruz

you have the right idea but are making a simple mistake.Express an equation in W and L equal to 20. You will then have two equations iin W and L.Solve and find W and LThen check so that givens are satisfied

bjh
• Feb 11th 2010, 08:44 AM
Soroban
Hello, mcruz65!

Quote:

An open rectangular gutter is made by turning up the sides of a piece of metal 20 in. wide.
The area of the cross-section of the gutter is 50 inē.
Find the depth of the gutter.

Code:

      *        *       |        |     D |        | D       |        |       * - - - - *           W

The depth of the gutter is $\displaystyle D.$
The width of the gutter is $\displaystyle W.$

We have: .$\displaystyle W + 2D \:=\:20 \quad\Rightarrow\quad W \:=\:20-2D$ .[1]

The area is 50 inē: .$\displaystyle DW \:=\:50$ .[2]

Substitute [1] into [2]: .$\displaystyle D(20-2D) \:=\:50$

. . which simplifies to: .$\displaystyle D^2 - 10D + 25 \:=\:0$

Factor: .$\displaystyle (D-5)(d-5) \:=\:0$

Therefore: .$\displaystyle D = 5$

The depth of the gutter is 5 inches.

• Feb 11th 2010, 10:06 AM
mcruz65