These questions are pertaining to College Algebra

Question

1) Working together, Sarah and Heidi can clean the garage in 2 hours. If they work alone, it takes Heidi 3 hours longer than it takes Sarah. How long would it take Heidi to clean the garage alone.

 

2) A hose can fill a swimming pool in 6 hours. Another hose needs 3 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool.

Answer 1

Hi Keissa, work problems are set up like:

 

1/a + 1/b = 1/c

 

Where a, b, and c are the amount of work needed to complete a task.

 

Here, together Sarah and Heidi can do the work in 2 hours, our c.

 

Let x be the time it takes Sarah to complete the work, our a.

 

Then it takes Heidi x + 3 to complete the work, our b.

 

This gives:

 

1 / x + 1 / (x + 3) = 1 / 2

 

Multiply the entire equation by: (x) * (x + 3) * 2, to remove the fractions. This gives:

 

2 * (x + 3) + 2 * x = x * (x + 3)

 

2x + 6 + 2x  = x² + 3x

 

4x + 6 = x² + 3x

 

Subtract 4x from both sides:

 

6 = x² - x

 

Subtract 6 from both sides:

 

x² - x - 6 = 0

 

Factor:

 

(x - 3) * (x + 2) = 0

 

Use the zero product rule to solve for x:

 

x - 3 = 0

 

x = 3

 

and 

 

x + 2 = 0

 

x = -2

 

We can discard the x = -2 solution because work cannot be negative.

 

Answer:

 

It would take Sarah 3 hours to clean the garage alone.

 

It would take Heidi 6 hours to clear the garage alone.

 

Check:

 

1 / 3 + 1 / 6 = 1 / 2

 

2/ 6 + 1 / 6 = 1 / 2

 

3 / 6 = 1 / 2

 

1 / 2 = 1 / 2

 

Values check.

 

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