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)

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.

Wow thanks for the quick reply(Rofl)