The time taken by 18 caterpillars to eat the entire Bush in Violetta's front yard is 20 hours.
What is the time taken?
Time taken is the inverse of the rate of work.
As it is given that the time taken by 15 caterpillars to eat all the leaves on the bush in Violetta's front yard is 24 hours, therefore, the rate at which the 15 caterpillars eat the leaves can be written as,
[tex]\rm Rate = \dfrac{\text{Number of Bush That caterpillars eat}}{\text{Time taken by the caterpillars}}[/tex]
[tex]\rm Rate = \dfrac{1}{24}[/tex]
Now, as it is the rate of 15 caterpillars, therefore, the rate of a single caterpillar can be written as,
[tex]\rm Rate = \dfrac{\frac{1}{24}}{15} = \dfrac{1}{24 \times 15}[/tex]
Now, the time taken by 18 caterpillars can be written as,
[tex]\rm Time\ taken = \dfrac{Work}{Rate \times 18}\\\\\rm Time\ taken = \dfrac{1}{\dfrac{1}{24 \times 15}\times 18}\\\\Time \taken = \dfrac{24 \times 15}{1 \times 18} = 20 \ hours[/tex]
hence, the time taken by 18 caterpillars to eat the entire Bush in Violetta's front yard is 20 hours.
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