SOLUTION: One roofer can put a neew roof on a house three times faster than another. Working together they can roof a house in 4 days. How long would it take the faster roofer working alone?

Question 98406This question is from textbook beginning and intermediate algebra
: One roofer can put a neew roof on a house three times faster than another. Working together they can roof a house in 4 days. How long would it take the faster roofer working alone? I need to know how to set up the problem then i can work it from there This question is from textbook beginning and intermediate algebra

Found 2 solutions by stanbon, checkley71:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
One roofer can put a neew roof on a house three times faster than another. Working together they can roof a house in 4 days. How long would it take the faster roofer working alone? I need to know how to set up the problem then i can work it from there
-------------------
1st roofer DATA:
Time = x days/job ; Rate = 1/x job/day
-------------------
2nd roofer DATA:
Time = 3x days/job ; Rate = 1/3x job/day
---------------
Working-together DATA:
Time = 4 day/job ; Rate = 1/4 job/day
------------------
EQUATION:
rate + rate = together rate
================
I'll let you solve it.
=================
Cheers,
Stan H.
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
X*3X/(X+3X)=4 X= THE TIME FOR THE FASTER ROOFER.
3X^2/4X=4 NOW CROSS MULTIPLY
3X^2=16X
3X^2-16X=0
X(3X-16)=0
X=0 A NON ANSWER.
3X-16=0
3X=16
X=16/3 DAYS FOR THE FASTER ROOFER.
3*16/3=16 DAYS FOR THE SLOWER ROOFER.
PROOF
16/3*16/(16/3+16=4
(256/3)/[(16+16*3)/3]=4
(256/3)/[(16+48)/3]=4
(256/3)/(64/3)=4
NOW INVERT THE DENOMINATOR & MULTIPLY
(256/3)(3/64)=4 CANCEL OUT THE 3s.
256/64=4
4=4

RELATED QUESTIONS
one roofer can put a new roof on a house three times faster than another. Working... (answered by chosenpoint)
one roofer can put a new roof on a house three times faster than another. Working... (answered by edjones)
one roofer can put a new roof on a house three times faster than another. working... (answered by ikleyn)
One roofer can put a new roof on a house three times faster than another. Working... (answered by Theo)
One roofer can put a new roof on a house three times faster than another. Working... (answered by josgarithmetic,ikleyn,greenestamps)
If one professional roofer can roof and house in six days and another roofer can do it in (answered by ptaylor)
an experienced roofer can work twice as fast as helper. working together, they can... (answered by Boreal)
Mary can roof their house in 4 days working alone, her husband can roof their house in 6... (answered by josmiceli)
Julius can paint a house three (3) times faster than Ruben. Working together, they can... (answered by stanbon)