Let
be the time it takes for pumps A, B, and C (respectively) to fill 1 tank. Then
![\begin{cases}\dfrac1a+\dfrac1b=\dfrac1{\frac65}=\dfrac56\\\\\dfrac1a+\dfrac1c=\dfrac1{\frac32}=\dfrac23\\\\\dfrac1b+\dfrac1c=\dfrac12\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%5Cdfrac1a%2B%5Cdfrac1b%3D%5Cdfrac1%7B%5Cfrac65%7D%3D%5Cdfrac56%5C%5C%5C%5C%5Cdfrac1a%2B%5Cdfrac1c%3D%5Cdfrac1%7B%5Cfrac32%7D%3D%5Cdfrac23%5C%5C%5C%5C%5Cdfrac1b%2B%5Cdfrac1c%3D%5Cdfrac12%5Cend%7Bcases%7D)
Now,
![\left(\dfrac1a+\dfrac1b\right)-\left(\dfrac1a+\dfrac1c\right)=\dfrac56-\dfrac23\implies\dfrac1b-\dfrac1c=\dfrac16](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac1a%2B%5Cdfrac1b%5Cright%29-%5Cleft%28%5Cdfrac1a%2B%5Cdfrac1c%5Cright%29%3D%5Cdfrac56-%5Cdfrac23%5Cimplies%5Cdfrac1b-%5Cdfrac1c%3D%5Cdfrac16)
Then
![\left(\dfrac1b+\dfrac1c\right)+\left(\dfrac1b-\dfrac1c\right)=\dfrac12+\dfrac16\implies\dfrac2b=\dfrac23\implies b=3](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac1b%2B%5Cdfrac1c%5Cright%29%2B%5Cleft%28%5Cdfrac1b-%5Cdfrac1c%5Cright%29%3D%5Cdfrac12%2B%5Cdfrac16%5Cimplies%5Cdfrac2b%3D%5Cdfrac23%5Cimplies%20b%3D3)
This means
![\dfrac1a+\dfrac13=\dfrac56\implies\dfrac1a=\dfrac12\implies a=2](https://tex.z-dn.net/?f=%5Cdfrac1a%2B%5Cdfrac13%3D%5Cdfrac56%5Cimplies%5Cdfrac1a%3D%5Cdfrac12%5Cimplies%20a%3D2)
and
![\dfrac13+\dfrac1c=\dfrac12\implies\dfrac1c=\dfrac16\implies c=6](https://tex.z-dn.net/?f=%5Cdfrac13%2B%5Cdfrac1c%3D%5Cdfrac12%5Cimplies%5Cdfrac1c%3D%5Cdfrac16%5Cimplies%20c%3D6)
Working together, all 3 pumps would operate at a rate of
![\dfrac1a+\dfrac1b+\dfrac1c=1](https://tex.z-dn.net/?f=%5Cdfrac1a%2B%5Cdfrac1b%2B%5Cdfrac1c%3D1)
or 1 tank in 1 hour, so the answer is D.
Assuming that he doesn't pay taxes on what he owes, then his remaining balance to pay is $819.48. I hope this helped.
Answer:
<h2>
11.4</h2>
Solution,
∆ ACB = ∆ EFD
finding the value of X,
![\frac{x}{3.8} = \frac{15}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B3.8%7D%20%20%3D%20%20%5Cfrac%7B15%7D%7B5%7D%20)
Apply cross product property
![x \times 5 = 15 \times 3.8](https://tex.z-dn.net/?f=x%20%5Ctimes%205%20%3D%2015%20%5Ctimes%203.8)
Calculate the product
![5x = 57](https://tex.z-dn.net/?f=5x%20%3D%2057)
Divide both sides by 5
![\frac{5x}{5} = \frac{57}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B5x%7D%7B5%7D%20%20%3D%20%20%5Cfrac%7B57%7D%7B5%7D%20)
Calculate
![x = 11.4](https://tex.z-dn.net/?f=x%20%3D%2011.4)
Hope this helps...
Good luck on your assignment...
Answer:
17
Step-by-step explanation:
Add 8 and 9 together .