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# intermediate algebra

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Two companies working together can clear a parcel of land in 26 hours.  Working alone, it would take Company A 10 hours longer to clear the land than it would Company B.  How long would it take Company B to clear the parcel of land alone?

Aug 6, 2019

#1
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Since the 2 companies together take 26 hours to finish.

Therefore:

A+B=26

"Company A takes 10 more hours than company B)

Therefore:

B-10(hours)=A

Subsitute A with B-10 in A+B=26

We get:

(B-10)+B=26

2B-10=26

2B=36

(Divide by 2)

B=18 hours

To get A= A+18=26

Subract 18

A=8 hours

It would take company B 18 hours to finish alone.

It would take company A 8 hours to finish alone.

Aug 6, 2019
#2
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Company A  = A

Company B  = B

Company A's hourly rate =1 / A = 1 / [26 + 10] =1 / 36

1 / A  +  1 / B = 1 / 26

1 / 36  +  1 / B = 1 / 26

1 / B = 1 / 26  - 1 / 36 [The LCM of 26 and 36 =468

1 / B = 18 / 468  -  13 / 468 =5 / 468 Company B's rate. Therefore, it would take Company B:

B =468/5 =93.6 hours to finish the job working alone! THIS IS THE CORRECT ANSWER!.

Check: 1/A + 1/B = 1/26

1/36  + 1/93.6 = 1/26

1 / 26 = 1 / 26

Aug 6, 2019
#3
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The second solution assumes that Company A would take 10 hours longer than the 2 Companies working together. But that is NOT what the question says. It says Co. A takes 10 hours longer than Co. B, when working alone! So the solution looks like this:

1/B + 1/(B+10) = 1/26

B =47.48 hours - for Co. B working alone to clear the land.

A =47.48 + 10 =57.48 hours - for Co. A to clear the land working alone.

So that: 1/47.48  +  1/57.48 =1/26, or 26 hours when both Companies work together.

Aug 6, 2019
#4
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Two companies working together can clear a parcel of land in 26 hours.  Working alone, it would take Company A 10 hours longer to clear the land than it would Company B.  How long would it take Company B to clear the parcel of land alone?

Thanks guests.

I struggle with these myself.  I decided to have a go.  I got the same as the last guest. Speed of A + Speed of B = speed of both together

$$speed=\frac{\text{Land to be cleared}}{time \;taken}$$

Let the land to be cleared be L

$$S_B=\frac{L}{t_B}\qquad \qquad S_A=\frac{L}{t_B+10} \qquad \qquad \\~\\ S_B+S_A=\frac{L}{26}\\ \frac{L}{t_B}+\frac{L}{t_B+10} =\frac{L}{26}\\ \frac{1}{t_B}+\frac{1}{t_B+10} =\frac{1}{26}\\ \text{It will be easier to follow if I let }Z=T_B\\ \qquad \frac{1}{Z}+\frac{1}{Z+10} =\frac{1}{26}\\ \qquad \frac{Z}{Z(Z+10)}+\frac{Z+10}{Z(Z+10)} =\frac{1}{26}\\ \qquad\frac{2Z+10}{Z(Z+10)} =\frac{1}{26}\\ \qquad 52Z+260=Z^2+10Z\\ \qquad Z^2-42Z-260=0\\ \qquad \text{Using the quadrativ euqation the answer is}\\ \qquad Z=21+\sqrt{701}\approx 47.48$$

so   On their own B will take 47.48 hours to clear the land.