Question

Emma drank \[\dfrac{1}{4}\] of a milk shake in \[\dfrac{1}{12}\] of a minute. How many minutes will it take her to drink a full milk shake?

Answer 1

Hint: We are given the rate at which Emma drinks milk shake. The question says Emma drinks \[\dfrac{1}{4}\] of a milk shake in \[\dfrac{1}{12}\] of a minute. And we have to find out how many minutes she will drink an entire milk shake. Since, the time taken by Emma to drink one full milk shake is asked so, we will use the unitary method to solve the question.

Complete step by step solution:
According to the given question, we are given that Emma drinks \[\dfrac{1}{4}\] of a milk shake in \[\dfrac{1}{12}\] of a minute and using this information we have to find the time taken by Emma to complete one full milk shake in minutes.
Since, the time taken by Emma to drink one full milk shake is asked so, we will use the unitary method to solve the question.
Unitary method is very helpful and handy while dealing to find a quantity equivalent to one entity from the given values of quantity for entities greater than one.
So, we have,
\[\dfrac{1}{4}\] of a milkshake is drunk by Emma in \[\to \dfrac{1}{12}\] of a minute
So, for 1 entire milk shake, the time taken is \[\to \dfrac{\dfrac{1}{12}}{\dfrac{1}{4}}\times 1\]
Calculating the expression further, we will have,
\[\Rightarrow \dfrac{4}{12}\times 1\]
Since, we know that any number or fraction multiplied by 1 gives the fraction or the number itself.
\[\Rightarrow \dfrac{4}{12}\]
Reducing the fraction further, we will get,
\[\Rightarrow \dfrac{1}{3}\]
Therefore, Emma will complete one full milk shake in \[\dfrac{1}{3}\] of a minute or we can say in 20 seconds.

Note: The unitary method applied should be done step wise. Also, \[\dfrac{1}{{}^{1}/{}_{a}}=a\] and \[\dfrac{{}^{1}/{}_{a}}{1}=\dfrac{1}{a}\]. While performing this reversal, the expression should be written correctly. And we can see that the question asked us to write the time taken in a minute so wrote it that way. If the question was asked to write the solution in hours, we will have to write as specified.