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Intermediate Algebra Word Problem
- Thread starter Josilyn08
- Start date
Hello, Josilyn08!
This can be solved with one equaton.
But it takes a bit of baby-talk to construct it
\(\displaystyle \text{The first hose fills the pool in 3 hours.}\)
\(\displaystyle \text{In one hour, it fills }\tfrac{1}{3}\text{ of the pool.}\)
\(\displaystyle \text{In }x\text{ hours, it fills }\tfrac{x}{3}\text{ of the pool.}\)
\(\displaystyle \text{The second hose fills the pool in 5 hours.}\)
\(\displaystyle \text{In one hour, it fills }\tfrac{1}{5}\text{ of the pool.}\)
\(\displaystyle \text{In }x\text{ hours, it fills }\tfrac{x}{5}\text{ of the pool.}\)
\(\displaystyle \text{The leak empties the pool in 11 hours.}\)
\(\displaystyle \text{In one hour, it empties }\tfrac{1}{11}\text{ of the pool.}\)
\(\displaystyle \text{In }x\text{ hours, it empties }\tfrac{x}{11}\text{ of the pool.}\)
\(\displaystyle \text{Working together for }x\text{ hours, they will fill }\,\frac{x}{3} + \frac{x}{5} - \frac{x}{11}\text{ of the pool.}\)
\(\displaystyle \text{But in }x\text{ hours, we expect the entire pool to be filled (1 pool).}\)
\(\displaystyle \text{There is our equation! }\;\hdots\quad \frac{x}{3} + \frac{x}{5} - \frac{x}{11} \:=\:1\)
\(\displaystyle \text{Multiply by 165: }\:55x + 33x - 15x \:=\:165 \quad\Rightarrow\quad 73x \:=\:165 \quad\Rightarrow\quad x \:=\:\frac{165}{73}\)
\(\displaystyle \text{The pool will be filled in: }\:2\tfrac{19}{73}\text{ hours} \;\;\approx\;\; \text{2 hours, 15 minutes, 37 seconds.}\)
This can be solved with one equaton.
But it takes a bit of baby-talk to construct it
A pool can be filled by one hose in 3 hours and by a second in 5 hours.
However, there is a leak in the pool which will empty the pool in 11 hours.
How long will it take both hoses to fill the pool?
\(\displaystyle \text{The first hose fills the pool in 3 hours.}\)
\(\displaystyle \text{In one hour, it fills }\tfrac{1}{3}\text{ of the pool.}\)
\(\displaystyle \text{In }x\text{ hours, it fills }\tfrac{x}{3}\text{ of the pool.}\)
\(\displaystyle \text{The second hose fills the pool in 5 hours.}\)
\(\displaystyle \text{In one hour, it fills }\tfrac{1}{5}\text{ of the pool.}\)
\(\displaystyle \text{In }x\text{ hours, it fills }\tfrac{x}{5}\text{ of the pool.}\)
\(\displaystyle \text{The leak empties the pool in 11 hours.}\)
\(\displaystyle \text{In one hour, it empties }\tfrac{1}{11}\text{ of the pool.}\)
\(\displaystyle \text{In }x\text{ hours, it empties }\tfrac{x}{11}\text{ of the pool.}\)
\(\displaystyle \text{Working together for }x\text{ hours, they will fill }\,\frac{x}{3} + \frac{x}{5} - \frac{x}{11}\text{ of the pool.}\)
\(\displaystyle \text{But in }x\text{ hours, we expect the entire pool to be filled (1 pool).}\)
\(\displaystyle \text{There is our equation! }\;\hdots\quad \frac{x}{3} + \frac{x}{5} - \frac{x}{11} \:=\:1\)
\(\displaystyle \text{Multiply by 165: }\:55x + 33x - 15x \:=\:165 \quad\Rightarrow\quad 73x \:=\:165 \quad\Rightarrow\quad x \:=\:\frac{165}{73}\)
\(\displaystyle \text{The pool will be filled in: }\:2\tfrac{19}{73}\text{ hours} \;\;\approx\;\; \text{2 hours, 15 minutes, 37 seconds.}\)