Question

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??

Answer 1

Let 

x---------------- > Terrence time to finish a word search

y----------------- > Charlotte time to finish a word search

z----------------- >  Frank  time to finish a word search

  we have that

 x=(3/4)*z

y=(2/3)*x

z=32

therefore

x=(3/4)*z----------- > (3/4)*32= 24 min-----> Terrence time to finish a word search

y=(2/3)*x------------ > (2/3)*24=16 min-----> Charlotte time to finish a word search

 The answer is 16 minutes

Answer 2

16 minutes

Further explanation

Given:

Terrence finished a word search in $\frac{3}{4}$ the time it took Frank.

Charlotte finished the word search in $\frac{2}{3}$ the time it took Terrence.

Frank finished the word search in 32 minutes.

Question:

How long did it take Charlotte to finish the word search?

The Process:

Step-1: find out how long Terrence took time 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:

$\boxed{8}\boxed{8}\boxed{8}\boxed{8} = 32 \ minutes$

$\boxed{1 \ unit = 8 \ minutes} \ from \ \boxed{ \ 32 \div 4 = 8 \ }$

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

$\boxed{8}\boxed{8}\boxed{8} = \ ? \ minutes$ or 3 of 4 units.

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

$\boxed{ \ 3 \ unit \times 8 \ minutes = 24 \ minutes \ }$

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:

$\boxed{8}\boxed{8}\boxed{8} = 24 \ minutes$

$\boxed{1 \ unit = 8 \ minutes} \ from \ \boxed{ \ 24 \div 3 = 8 \ }$

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

$\boxed{8}\boxed{8} = \ ? \ minutes$ or 2 of 3 units.

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

$\boxed{ \ 2 \ unit \times 8 \ minutes = 16 \ minutes \ }$

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

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

- - - - - - - - - -

Quick Steps

Frank = in 32 minutes.

Step-1:

$Terrence = \frac{3}{4} \ of \ Frank$

$\boxed{ \ Terrence = \frac{3}{4} \times 32 \ minutes \ }$

We crossed out 4 and 32.

$\boxed{ \ Terrence = 3 \times 8 \ minutes \ }$

$\boxed{\boxed{ \ Terrence = 24 \ minutes \ }}$

Step-2:

$Charlotte = \frac{2}{3} \ of \ Terrence$

$\boxed{ \ Charlotte = \frac{2}{3} \times 24 \ minutes \ }$

We crossed out 3 and 24.

$\boxed{ \ Charlotte = 2 \times 8 \ minutes \ }$

$\boxed{\boxed{ \ Charlotte = 16 \ minutes \ }}$

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