hey i have 2 problems that i need help with... work rate word problems...

Dan can carpet his house in 9 hours. Mike can carpet the same house in 13 hours. How long would it take them to lay the carpet if they worked together?

Jones Conctruction company crew needs 28 hours to do a job. Smith contruction company needs 34 hours to do the same job. If both crews work for 9 hours, how long will it take the Smith conctrucion company to finish the job alone?

thanks!! postscript: th last one doesnt make sense to me ... but thats the way my teacher wrote it!!

GAR

2. Originally Posted by eah1010
hey i have 2 problems that i need help with... work rate word problems...

Dan can carpet his house in 9 hours. Mike can carpet the same house in 13 hours. How long would it take them to lay the carpet if they worked together?
20 hours

I like to do these problems like this: In one hour Dan does $\frac{1}{9}$ of the carpet and Mike does $\frac{1}{13}$ hours. Thus, together in exactly one hour they do $\frac{1}{9}+\frac{1}{13}=\frac{22}{117}$ of the carpet. Thus, make the propertion if in 1 hour they do $22/117$ of the carpet, then how much for the full carpet. In proportion terms,
$\frac{\frac{22}{117}\mbox{ fraction of the carpet }}{1 \mbox{ hour }}=\frac{1 \mbox{ fraction of the carpet}}{x \mbox{ hours }}$
Cross multiply,
$\frac{22}{117}x=1$
Solve, $x=\frac{117}{22}=5\frac{7}{22}$
-----------------------------------
I developed a formula:
If it takes a person $a$ hours to do a job and it takes another $b$ hours to do the job then together it takes them $\frac{ab}{a+b}$
You can use this to solve your problem.

3. thank you so much!! that formula really deos help!!

GAR

4. Originally Posted by eah1010
Jones Conctruction company crew needs 28 hours to do a job. Smith contruction company needs 34 hours to do the same job. If both crews work for 9 hours, how long will it take the Smith conctrucion company to finish the job alone?

thanks!! postscript: th last one doesnt make sense to me ... but thats the way my teacher wrote it!!

GAR
First understand the situation. It takes Jones Company 28 hours and Smith Company 34 hours. They start working together for 9 hours. After 9 hours Jones Company stops and leaves the rest of the job full Smith Company to finish.

I am going to use the formula I developed in the problem before. In this case, the amount of time of them to work together is,
$\frac{28\cdot 34}{28+34}=\frac{952}{62}=\frac{476}{31}$ hours.
Now, we find the fraction of the full work they did in 9 hours, we set up a proportion,
$\frac{1 \mbox{ fractional work }}{\frac{476}{31}\mbox{ hours }}=\frac{x\mbox{ fractional work }}{9 \mbox{ hours }}$
Thus, cross multiply,
$\frac{476}{31}x=9$
Thus,
$x=\frac{279}{476}$
Thus,
$\frac{197}{476}$ of the work remains to be done by Smith. Now set up another proportion.
$\frac{1\mbox{ fractional part }}{34\mbox{ hours }}=\frac{\frac{279}{476}\mbox{ fractional part }}{x\mbox{ hours }}$.
Cross multiply,
$x=34\cdot\frac{279}{476}=19.9\frac{}{285714}$ hours.

5. Originally Posted by eah1010
thank you so much!! that formula really deos help!!

GAR
Welcome,