# College Algebra word problem help

• February 28th 2008, 12:59 PM
fatbob91
College Algebra word problem help
First time posting so here goes. Would like to know how to solve.

1. It takes Jake 10 hrs to paint a house. When his friend Betty helps it takes 6 hours to paint the same house. How long does it take for betty paint the house alone?

2. A carpet amnufacturer blends 2 fibers one 20 percent wool and the second 50 percent wool, how many pounds of each fiber should be woven to produce 500lbs that is 35 percent wool?

Thanks(Hi)
• February 28th 2008, 01:09 PM
Mathnasium
For the first one, think about how much they can do in one hour and together. If it takes, for example, 4 hours to do a job, then in one hour you can do 1/4 of the job, right?

So, in one hour, Jake can do 1/10th of the job. Betty can do 1/x of the job (i.e., she can do the whole job in x hours.) If they work together they can do 1/6 of the job. Another way of representing the hourly amount they can get done when working together is simply to add 1/10 + 1/x.

This gives $\frac{1}{10} + \frac{1}{x} = \frac{1}{6}$. Using 30 as a common denominator:

$\frac{3}{30}+\frac{1}{x}=\frac{5}{30}$ -->

$\frac{1}{x} = \frac{2}{30} = \frac{1}{15}$, so x = 15.

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#2)

Let's say he uses x pounds of the 20% wool fiber. Then the amount of wool fiber from that type of cloth or carpet or what-have-you is (.20)*x.

Now, if he used x pounds of the 20%, he must use 500-x of the 50% fiber (since he used 500 pounds total). The wool from the 50%-type can be expressed, then, as (.50)(500-x).

We also know that the total wool in the final, 500 pounds can be written as (.35)*500.

If we take the wool from the 20%, add it to the wool from the 50%, it should equal the wool in the 35% mixture.

This gives:

.2x + 250 -.5x = 175.

Solving for x gives 250. So he uses 250 of one fiber, 250 of the other.

This makes sense since 35% is exactly halfway between 20 and 50. Thus, he should use half of each.
• February 28th 2008, 01:45 PM
fatbob91
Wow thanks for the quick reply(Rofl)