Terrence finished a word search in 3/4 the time it took Frank. Charlotte finished the word search in 2/3 the time it took Terrence. Frank finished the word search in 32minutes. How long did it take Charlotte to finish the word search??

Looking at the relationship between Terrence and Frank in finishing a word search, we can make the appropriate diagram for the time Frank took as follows:

[tex]\boxed{8}\boxed{8}\boxed{8}\boxed{8} = 32 \ minutes[/tex]

[tex]\boxed{1 \ unit = 8 \ minutes} \ from \ \boxed{ \ 32 \div 4 = 8 \ }[/tex]

Terrence finished the word search in [tex]\frac{3}{4}[/tex] the time it took Frank, therefore the diagram for Terrence's is as follows:

[tex]\boxed{8}\boxed{8}\boxed{8} = \ ? \ minutes[/tex] or 3 of 4 units.

Let us count the time Terrence took to finish the word search.

[tex]\boxed{ \ 3 \ unit \times 8 \ minutes = 24 \ minutes \ }[/tex]

Therefore, it took Terrence 24 minutes to finish the word search.

Step-2: find out how long Charlotte took time to finish the word search

Looking at the relationship between Charlotte and Terrence in finishing a word search, we can make the appropriate diagram for the time Terrence took as follows:

[tex]\boxed{8}\boxed{8}\boxed{8} = 24 \ minutes[/tex]

[tex]\boxed{1 \ unit = 8 \ minutes} \ from \ \boxed{ \ 24 \div 3 = 8 \ }[/tex]

Charlotte finished the word search in [tex]\frac{2}{3}[/tex] the time it took Terrence, therefore the diagram for Charlotter's is as follows:

[tex]\boxed{8}\boxed{8} = \ ? \ minutes[/tex] or 2 of 3 units.

Let us count the time Charlotte took to finish the word search.

[tex]\boxed{ \ 2 \ unit \times 8 \ minutes = 16 \ minutes \ }[/tex]

Therefore, it took Charlotte 16 minutes to finish the word search.

Thus, Charlotte took 16 minutes to finish the word search.

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Quick Steps

Frank = in 32 minutes.

Step-1:

[tex]Terrence = \frac{3}{4} \ of \ Frank[/tex]

[tex]\boxed{ \ Terrence = \frac{3}{4} \times 32 \ minutes \ }[/tex]

We crossed out 4 and 32.

[tex]\boxed{ \ Terrence = 3 \times 8 \ minutes \ }[/tex]

[tex]\boxed{\boxed{ \ Terrence = 24 \ minutes \ }}[/tex]

Step-2:

[tex]Charlotte = \frac{2}{3} \ of \ Terrence[/tex]

[tex]\boxed{ \ Charlotte = \frac{2}{3} \times 24 \ minutes \ }[/tex]

We crossed out 3 and 24.

[tex]\boxed{ \ Charlotte = 2 \times 8 \ minutes \ }[/tex]

[tex]\boxed{\boxed{ \ Charlotte = 16 \ minutes \ }}[/tex]

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