Purchase Solution

Quadratic Equation Word Problems

Not what you're looking for?

Ask Custom Question

1. A rectangular garden has dimensions of 15 feet by 11 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 192 square feet?

2. A business invests $8,000 in a savings account for two years. At the beginning of the second year, an additional $2,500 is invested. At the end of the second year, the account balance is $11,445. What was the annual interest rate?

3. Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle.

4. The Hudson River flows at a rate of 5 miles per hour. A patrol boat travels 40 miles upriver, and returns in a total time of 6 hours. What is the speed of the boat in still water?

Purchase this Solution

Solution Summary

This solution is comprised of an extensive explanation of step by step equations for each of the four problems.

Solution Preview

Please refer to the attached file for the complete and formatted solution.

1) The length of the rectangular garden is 15 feet and the width of the garden is 11 feet.
Thus the area of the garden is 165.

Now there is a gravel path of uniform path is to be built around the garden.

Suppose the uniform width of the gravel path be "x" feet
Thus, the length of the garden including the gravel path = (15 + 2x) feet and the width of the garden including the gravel path = (11+ 2x) feet
This means the area of the gravel path is
(15+ 2x) (11 + 2x) - Area of the garden

This is equal to:

(15 + 2x)(11 + 2x) -165
165 + 30x + 22x + 4x2 -165
52x + 4x2
Now, the given area of the gravel is 192 square feet

So, the equation becomes
52x + 4x2 = 192
4 x2 + 52x =192
4x2 + 52x - 192 =0
Taking 4 common from the equation, we get--
x2 + 13x -48 =0
x2 + 16x -3x -48 =0
Now taking "x" common from (x2 + 16x) and "-3" common from (-3x -48), we have—
x(x +16) -3(x+16) = 0

(x- 3)(x+16)=0
This means
x= 3 because -16 is not acceptable

the uniform width of the gravel is 3 feet.

2) Let r be the annual interest rate.
Now, according to the formula,
Interest = Principal * Rate * Time
- for the first year, we have
Principal= $8000
So, Interest in first year = 8000*r *1 = 8000r
Thus, the amount after ...

Purchase this Solution


Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Probability Quiz

Some questions on probability

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.