|
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):
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.
|
|
|
| |
