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Question 1103450: Two companies working together can clear a parcel of land in 27 hours . Working alone it would take company A 2 hours longer to clear the land than it would Company B to clear the parcel of land alone?
Found 2 solutions by greenestamps, richwmiller:
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
The setup for the problem is straightforward, using the standard algebraic process. But I suspect the numbers in the problem are wrong, because the answers are irrational numbers. Worthwhile problems like this have answers that are rational numbers.
Let x be the number of hours it takes company B to do the job; then x+2 is the number of hours company A takes.
Then the fractions of the job that the two companies do in 1 hour are 1/x and 1/(x+2). And since together the two companies together do 1/27 of the job in 1 hour,
I won't take this any further, because, as I have said, the answers are unreasonable for a problem of this type.
Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! 1/x+1/(x+2)=1/27
(27*x*(x+2))/x+(27*x*(x+2))/(x+2)=(27*x*(x+2))/27
(27*(x+2))+27*x=x*(x+2)
27*x+54+27*x=x^2+2*x
54*x+54=x^2+2*x
x^2-52*x-54=0
Can it be factored?
What factors of -54 add up to -52?
Nevertheless, we will complete the square.
x^2-52*x=54
Add it.
x^2-52*x+(-52/2)=54+(-52/2)
Square it.
x^2-52*x+(2704/4)=54+(2704/4)
x^2-52*x+(676)=54+(676)
x^2-52*x+(676)=730
(x-26)^2=730
(x-26)^2=730
We will continue.
x+-26=(+-)27.0185122
x=26(+-)27.0185122
Positive useful answer:
x=26+27.0185122
Company B x=53.0185122
x+2=2+53.0185122
x+2=55.0185122
Company A =55.0185122
check
1/x+1/(x+2)=1/27
1/53.0185122+1/(53.0185122+2)=1/27
1/53.0185122+1/55.0185122=1/27
55.0185122/2916.99966+53.0185122/2916.99966=1/27
108.037024/2916.99966=1/27
0.37037037e-1=0.37037037e-1
ok
Useless answer:
x=26-27.0185122
Useless answer is x=-1.01851217
x =-1.01851217
This answer is useless because it is Negative
For real life cases involving time, distance and other measurements, we reject the negative results
codewtp
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