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Makovka662 [10]
2 years ago
6

John is trying to drain a swimming pool. He has two pumps, but he can only use one at a time. He knows that the time a pump take

s to drain the pool varies inversely with the power in watts of the pump. His old pump is a 80 watt pump, and it can drain the pool in 5 hours. How long would the job take if he uses his new 100 watt pump?
Mathematics
2 answers:
a_sh-v [17]2 years ago
8 0
It would take 6 \frac{1}{4} hours or 6.25 hours if John uses the 100 watt pump.
Grace [21]2 years ago
3 0
\bf \begin{array}{llllll}
\textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\
\textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\
y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x}
\\
&&y=\cfrac{{{ k}}}{x}
\end{array}\\\\
-----------------------------\\\\


\bf \textit{the time a pump drains the pool varies inversely with the wattage }
\\\\\\
thus\qquad t=\cfrac{k}{w}\qquad 
\begin{cases}
t=time\\
k=\textit{constant of variation}\\
w=\textit{wattage power}
\end{cases}
\\\\\\
\textit{now, we know that with the old pump }
\begin{cases}
w=80\\
t=5
\end{cases}\implies 5=\cfrac{k}{80}
\\\\\\
5\cdot 80=k\implies 400=k\qquad thus\implies \boxed{y=\cfrac{400}{w}}

now, how long will it take with the new pump that does 100watts?

well, set w = 100, to get the "t" value
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