SOLUTION: An experienced roofer can roof a house in 26 hours. A beginning roofer needs 39 hours to complete the same job. Find how long it takes for the two of them to do the job together.

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Question 287709: An experienced roofer can roof a house in 26 hours. A beginning roofer needs 39 hours to complete the same job. Find how long it takes for the two of them to do the job together.
This is what i know:
I think I need to use direct or inverse variation equations
This is what I've tried:
y=k/x
26=k/39--Multiple by 39 to get k by itself
1014=k
The back of my textbook says the answer is 15.6 hours

Thank you for your time.
This homework is due tomorrow.
I'm grateful for any help I can get
Thanks again
Found 4 solutions by tinkerbell146, ankor@dixie-net.com, stanbon, richwmiller:
Answer by tinkerbell146(2)   (Show Source):
You can put this solution on YOUR website!
use this equation to solve
1/26+1/39=1/t

Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!
An experienced roofer can roof a house in 26 hours.
A beginning roofer needs 39 hours to complete the same job.
Find how long it takes for the two of them to do the job together.
:
Here is how I would do it:
let t = time required for them to complete the job together
:
let 1 = the completed job
:
Each does a fraction of the job, the two fractions add up to 1
:
+ = 1
multiply equation by 1014 (that's 26*39), results
39t + 26t = 1014
65t = 1014
t =
t = 15.6 hrs
:
:
Check solution by find the faction that each does
15.6/26 + 15.6/39 =
.6 + .4 = 1

Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
An experienced roofer can roof a house in 26 hours. A beginning roofer needs 39 hours to complete the same job. Find how long it takes for the two of them to do the job together
----------
Experienced rate = 1/26 roof/hr
---
Beginner rate = 1/39 roof/hr
-------
Together rate = 1/x roof/hr
----------------------------------
Equation:
rate + rate = together rate
1/26 + 1/39 = 1/x
---
Multiply thru by 26*39x to get:
39x + 26x = 26*39
65x = 26*39
x = 78/5 = 15.6 hrs. (time to finish the roof if they work together)
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Cheers,
Stan H.

Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website!
Several other tutors gave you excellent answers.
I want to thank you for giving the books answer and your attempt at solving the problem.