Question

if 7 cats kill 7 rats in 7 minutes how many would be needed to kill hundred and fifty minutes​

Answer 1

Question: 7 cats kill 7 rats in 7 minutes. How many cats would be needed to kill 100 in 50 minutes?

Required answer: 14 cats.

Solution

7 cats kill 7 mouses in 7 minutes. This means 1 cat kills 1 mouse in 7 minutes. The work rate of each cat is $\dfrac{1}{7}$.

Since,

$\text{work rate}=\dfrac{\text{work done}}{\text{time}}$

So,

$\text{work rate of a cat}=\dfrac{\text{kills}}{\text{time}}$

And also,

$\text{kills}=\text{work rate of a cat}\times \text{time}$

Which gives,

$\bigstar\text{total kills}=\text{work rate of a cat}\times \text{time}\times \text{the number of cats}$

What we are given are,

• $\text{total kills}=100\ \text{kills}$
• $\text{work rate of a cat}=\dfrac{1}{7}\ \text{kills per minute}$
• $\text{time}=50\ \text{minutes}$

Let's assign an unknown to the number of cats.

$\bigstar\text{number of cats}=x\ \text{cats}$

We already have an equation.

$\bigstar\text{total mouses killed}=\text{work rate of a cat}\times \text{time}\times \text{the number of cats}$

Then,

$\implies 100=\dfrac{1}{7} \times 50\times x$

$\implies x=100\times 7\times \dfrac{1}{50}$

$\implies x=14\ \text{cats}$

So, 14 cats are needed.