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I can't figure this problem. Can anyone help me understand asap?? thanks!
- Thread starter emilyd126
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Hint:
1) What do you need to find? ...... Time/s to fill the tank individually by the inlet-pipe and the hose.
2) Assign variable names to each of the finds. Let:
Time to fill the tank individually by the inlet-pipe = I
Time to fill the tank individually by the hose = H
Now continue.....
Please share your work/thoughts with us so that we know where to begin to help you.
HallsofIvy
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"A Chinese Restaurant has a goldfish pond. Suppose that an inlet pipe and a hose together can fill the pond in 3 hours. The inlet pipe alone can complete the job in one hour less than the hose alone. Find the time that the hose can complete the job alone and the time that the inlet pipe can complete the job alone."
When two pipes (or two machines or two people, etc.) work together, their rates of work add.
Let "T" be the time, in hours, in which the hose alone could fill the pond. Its rate is 1/T "pond per hour". We are told that the inlet pipe can fill the pond in one hour less: T-1. So its rate of work is 1/(T-1) "pond per hour". When both are used their rate of filling the pond is \(\displaystyle \frac{1}{T}+ \frac{1}{T- 1}= \frac{T-1}{T(T-1)}+ \frac{T}{T(T-1)}= \frac{2T- 1}{T(T-1)}\). We are told that, with the two together they fill the pond in 3 hours so their rate of filling is 1/3 "pond per hour".
\(\displaystyle \frac{2T- 1}{T(T-1)}= \frac{1}{3}\). Multiply on both sides by \(\displaystyle 3T(T-1)\) to get
\(\displaystyle 3(2T- 1)= T(T- 1)\)
\(\displaystyle 6T- 3= T^2- T\)
\(\displaystyle T^2- 7T+ 3= 0\).
Solve that quadratic equation for T. There will be two roots but the fact that both T and T-1 must be positive eliminates one of the roots.
When two pipes (or two machines or two people, etc.) work together, their rates of work add.
Let "T" be the time, in hours, in which the hose alone could fill the pond. Its rate is 1/T "pond per hour". We are told that the inlet pipe can fill the pond in one hour less: T-1. So its rate of work is 1/(T-1) "pond per hour". When both are used their rate of filling the pond is \(\displaystyle \frac{1}{T}+ \frac{1}{T- 1}= \frac{T-1}{T(T-1)}+ \frac{T}{T(T-1)}= \frac{2T- 1}{T(T-1)}\). We are told that, with the two together they fill the pond in 3 hours so their rate of filling is 1/3 "pond per hour".
\(\displaystyle \frac{2T- 1}{T(T-1)}= \frac{1}{3}\). Multiply on both sides by \(\displaystyle 3T(T-1)\) to get
\(\displaystyle 3(2T- 1)= T(T- 1)\)
\(\displaystyle 6T- 3= T^2- T\)
\(\displaystyle T^2- 7T+ 3= 0\).
Solve that quadratic equation for T. There will be two roots but the fact that both T and T-1 must be positive eliminates one of the roots.
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