Mathematics: 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 takes 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?

John is trying to drain a swimming pool. he has

Ответ:

breiajr

13.01.2022

$\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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Ответ:

cristianTalonzo

16.01.2022

Mathematics

Step-by-step explanation:

X = cost of PB

Y = cost of J

6X + 4Y = 1932 <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies

Dividing everything in the first equation by 2:

3X + 2Y = 966 <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies

Elimination method... let's multiply the first equation by 3 and the second equation by -2.

9X + 6Y = 2898

-10X + -6Y = -3134

-X = -236

X = 236 --> so the price of the PB is 236 pennies or $2.36

Plugging into the second equation as the numbers are a bit smaller,

5X + 3Y = 1567

5(236) + 3Y = 1567

1180 + 3Y = 1567

3Y = 387

Y = 129. So the price of the jelly is 129 pennies or $1.29.

Now we check: 4 x $1.29 + 6*2.36 = $19.32

3 x $1.29 + 5 x 2.36 = $15.37

The answers are verified and highlighted in bold.

6X + 4Y = 1932 <--- price is in pennies

5X + 3Y = 1567 <--- price in pennies

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