SOLUTION: Working together, a painter and the painter's apprentice can paint a room in 4h. Working alone, the apprentice requires 7 more hours to paint the room that the painter requires wor
Algebra.Com
Question 149944: Working together, a painter and the painter's apprentice can paint a room in 4h. Working alone, the apprentice requires 7 more hours to paint the room that the painter requires working alone. How long does it take the painter, working alone, to paint the room? Please round your answer to one decimal place.
4/T + 4/T+7 = 1
T(T+7)(4/T + 4/T+7) = T(T+7)1
(T+7)4+4T = T(T+7)
4T +28 +4T = T^2 +T7
8T+28=T^2+T7
Am I doing this right? I keep coming up with the wrong answer, I think.
Found 2 solutions by scott8148, stanbon:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
subtracting 8T+28 __ 0=T^2-T-28
using quadratic formula __ T=[1ħsqrt(1-(4*1*(-28)))]/2 __ T=[1ħsqrt(113)]/2
T=5.82 (approx)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Working together, a painter and the painter's apprentice can paint a room in
4 hours.
Time = 4 hrs/job ; Rate = 1/4 job/hr.
----------------------------------------------------
Working alone, the apprentice requires 7 more hours to paint the room than the painter requires working alone.
Painter's DATA:
Time = x hrs/job ; Rate = 1/x job/hr.
----------
Apprentice DATA:
Time = (x+7) hr/job ; Rate = 1/(x+7) job/hr
----------------------------------------
How long does it take the painter, working alone, to paint the room?
Please round your answer to one decimal place.
EQUATION:
rate + rate = together rate
1/x + 1/(x+7) = 1/4
Multiply thru by 4x(x+7) to get:
4(x+7) + 4x = x(x+7)
4x+28 + 4x = x^2+7x
x^2 -x -28 = 0
x = [1 +- sqrt(1-4*-28)]/2
Positive solution:
x = [1 + sqrt(29)]/2
x = 3.2 hrs (Painter's time to do the job)
x+7 = 10.2 hrs (Apprentices's time to do the job)
===============
Cheers,
Stan H.
RELATED QUESTIONS
A painter can paint a room three hours less than an apprentice. Together they can pain... (answered by Mathtut,gonzo)
A day laborer takes three more days to paint a house than an apprentice painter. A master (answered by ptaylor)
an experienced painter can paint a garage twice as fast as his apprentice. working... (answered by rwm)
How do I solve this? Can you show me the work as well? I am lost. Thank you.
Working... (answered by josgarithmetic)
One painter takes 6 hours longer to paint a room than does a second painter. Working... (answered by stanbon)
A painter can paint a wall in 20 minutes. Working alone, the painter's apprentice can can (answered by courtneycheyenne)
a painter can paint a fence in 12 hours working alone, his apprentice who works slower... (answered by KMST)
Painter Painter has three employees: Huey, Dewey, and Louie. Working together they can... (answered by swincher4391)
A master painter can paint the room in 5 hours, while his apprentice can do the same job... (answered by Boreal)