SOLUTION: I dont understand what we have to do for this problem. Working alone, Anton can install a brick patio in 2 hours less than Bill. Together Anton and Bill can install the patio in

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Question 128327This question is from textbook algebra structure and method
: I dont understand what we have to do for this problem.
Working alone, Anton can install a brick patio in 2 hours less than Bill. Together Anton and Bill can install the patio in 4 hours. To the nearest tenth of an hour, how long does it take Bill to install the patio working alone? This question is from textbook algebra structure and method

Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
All this says is that if you take any 2 people who are
able to do a certain job, one of them usually works
faster than the other, but if you are able to put
both of them to work on the same job, then they will
get it done faster than even the faster person
could do it alone.
In words,
(Anton's rate of working) + (Bill's rate of working) =
(their rate of working together)
And in more exact words,
{1 patio)/(Anton's time) + (1 patio)/(Bill's time) =
(1 patio)/ (their times working together)
Now with numbers:
Let A = Anton's time working alone
Let B = Bill's time working alone
A+=+B+-+2
1%2FA+%2B+1%2FB+=+1%2F4
multiply both sides of the equation by 4AB
4B+%2B+4A+=+AB
4B+%2B+4%28B+-+2%29+=+%28B+-+2%29%2AB
4B+%2B+4B+-+8+=+B%5E2+-+2B
B%5E2+-+10B+%2B+8+=+0
complete the square
B%5E2+-+10B+%2B+25+=+-8+%2B+25
B+-+5%29%5E2+=+17
B+-+5+=+sqrt%2817%29
B+=+sqrt%2817%29+%2B+5
B+=+9.123
The other solution is
B+=+-sqrt%2817%29+%2B+5 since there are 2 square roots (+) and (-)
B+=+.877
The larger number is the only one that makes sense
Bill takes 9.1 hours working alone
check answer:
A+=+B+-+2
A+=+9.123+-+2
A+=+7.123
1%2F7.123+%2B+1%2F9.123+=+1%2F4
.14039+%2B+.10961+=+.25
.250003+=+.25 close enough

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Working alone, Anton can install a brick patio in 2 hours less than Bill. Together Anton and Bill can install the patio in 4 hours. To the nearest tenth of an hour, how long does it take Bill to install the patio working alone?
-----------------------------
Bill DATA:
Time = x hrs/job ; Rate = 1/x job/hr
-----------------------------------
Anto DATA:
Time = (x-2) hrs/job ; Rate = 1/(x-2) job/hr
---------------------------
Together DATA:
Time = 4 hrs/job ; Rate = 1/4 job/hr
=======================================
EQUATION:
rate + rate = together rate
1/x + 1/(x-2) = 1/4
Multiply thru by 4x(x-2) to get:
4(x-2) + 4x = x(x-2)
8x - 8 = x^2-2x
x^2-10x+8 = 0
x = [10 +- sqrt(100-4*8)]/2
x = [10 +- sqrt(68)]/2
Positive answer:
x = (10 + sqrt(68))/2
x = 9.1231 hrs (Time is takes Bill to do the job)
=====================
Cheers,
Stan H.