Answer :
Given :
Challenge given is to volunteer for about 1 1/2 hours per week .
Autum did at a rate of 6 3/4 hours per week .
To Find :
The comparison ( ratio ) her volunteers rate with the challenge rate .
Solution :
Simplifying challenge rate in in normal fraction , [tex]1\dfrac{1}{2}=\dfrac{2+1}{2}=\dfrac{3}{2}[/tex] .
Also , simplifying her rate , [tex]6\dfrac{3}{4}=\dfrac{(6\times 4)+3}{4}=\dfrac{27}{4}[/tex] .
Now , ratio of his work by challenge is :
[tex]R=\dfrac{\dfrac{27}{4}}{\dfrac{3}{2}}\\\\\\R=\dfrac{27\times 2}{4\times 3}\\\\R=\dfrac{9}{2}[/tex]
Therefore , the ratio is 9/2 or 4 1/2 .
Hence , this is the required solution .