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

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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 [tex]\dfrac{1}{7}[/tex].

   Since,

   [tex]\text{work rate}=\dfrac{\text{work done}}{\text{time}}[/tex]

   So,

   [tex]\text{work rate of a cat}=\dfrac{\text{kills}}{\text{time}}[/tex]

   And also,

   [tex]\text{kills}=\text{work rate of a cat}\times \text{time}[/tex]

   Which gives,

   [tex]\bigstar\text{total kills}=\text{work rate of a cat}\times \text{time}\times \text{the number of cats}[/tex]

   What we are given are,

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

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

   [tex]\bigstar\text{number of cats}=x\ \text{cats}[/tex]

   We already have an equation.

   [tex]\bigstar\text{total mouses killed}=\text{work rate of a cat}\times \text{time}\times \text{the number of cats}[/tex]

   Then,

   [tex]\implies 100=\dfrac{1}{7} \times 50\times x[/tex]

   [tex]\implies x=100\times 7\times \dfrac{1}{50}[/tex]

   [tex]\implies x=14\ \text{cats}[/tex]

   So, 14 cats are needed.

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