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notsponge [240]

3 years ago

9

Plzzzz someone help

2 answers:

kiruha [24]3 years ago

8 0

All you have to do is subtract

Korvikt [17]3 years ago

3 0

Answer:

oof oof oof oof oof oof oof

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If 12 cats can catch 6 rats in 2 hours, how many hours would it take 50 cats to catch 75 rats?

sleet_krkn [62]

Answer:

50 cats would take 6 hours to catch 75 rats.

Step-by-step explanation:

After reading the statement we noticed the existence of two relationships:

1) <em>The amount of cats is directly proportional to the quantity of caught rats.</em>

2) <em>The amount of cats is inversely proportional to time taken to catch rats. </em>

That is to say:

$n \propto \frac{x}{y}$

$n = k\cdot \frac{x}{y}$ (Eq. 1)

Where:

$n$ - Amount of cats, dimensionless.

$x$ - Amount of caught rats, dimensionless.

$y$ - Time, measured in hours.

$k$ - Proportionality ratio, measured in hours.

Then, we obtain the following relationship by eliminating the proportionality ratio in (Eq. 1):

$\frac{n_{1}\cdot y_{1}}{x_{1}} = \frac{n_{2}\cdot y_{2}}{x_{2}}$ (Eq. 2)

Where:

$n_{1}$ , $n_{2}$ - Initial and final amounts of cats, dimensionless.

$x_{1}$ , $x_{2}$ - Initial and final amounts of caught rats, dimensionless.

$y_{1}$ , $y_{2}$ - Initial and final times, measured in hours.

Now we clear final time in (Eq. 2):

$y_{2} = y_{1}\cdot \left(\frac{n_{1}}{n_{2}} \right)\cdot \left(\frac{x_{2}}{x_{1}} \right)$

By knowing that $y_{1} = 2\,h$ , $n_{1} = 12$ , $x_{1} = 6$ , $n_{2} = 50$ , $x_{2} = 75$ , then we get that time taken by 50 cats to catch 75 rats is:

$y_{2} = (2\,h)\cdot \left(\frac{12}{50} \right)\cdot \left(\frac{75}{6}\right)$

$y_{2} = 6\,h$

50 cats would take 6 hours to catch 75 rats.

7 0

4 years ago