Question

A tanks length is 3 feet longer than its width. The height is 1 foot less than the width. The volume of the tank is 160 cubic feet. What is the width of the tank?

Answer 1

Answer:

The width of the tank is 5 feet.

Step-by-step explanation:

Let the width of the tank be $w ft$.

Then, the length of the tank will be $l=(w+3)ft$

and the heigth will be $h=(w-1)ft$.

It was given that the volume of the tank is $160ft^3$.

Recall that the tank is a cuboid or a rectangular prism.

The volume is given by;

$V=l\timesb \times w \times h$.

We substitute the given values into the formula to obtain;

$160=(w+3)(w)(w-1)$

We expand to obtain

$160=w(w^2-w+3w-3)$

$160=w(w^2+2w-3)$

$160=w^3+2w^2-3w$

$w^3+2w^2-3w-160=0$

$\Rightarrow w=5$

Therefore the width of the tank is 5 feet.