Given that,
The time taken by each girl in the race is given by,
Barbara:
[tex]=3\frac{3}{10}\text{ minutes}[/tex]Donna:
[tex]=2\frac{4}{5}\text{ minutes}[/tex]Cindy:
[tex]=x\text{ minutes}[/tex]Nicole
[tex]2\frac{1}{10}\text{ minutes}[/tex]1) Each girl ran one part of the race.
Total time taken is,
[tex]\begin{gathered} 11\frac{3}{5}\text{ minutes} \\ \end{gathered}[/tex]we get that,
[tex]3\frac{3}{10}+2\frac{4}{5}+x+2\frac{1}{10}=11\frac{3}{5}[/tex][tex]\frac{33}{10}+\frac{14}{5}+x+\frac{21}{10}=\frac{58}{5}[/tex][tex]\frac{33+(14\times2)+21}{10}+x=\frac{58}{5}[/tex][tex]\frac{33+28+21}{10}+x=\frac{58}{5}[/tex][tex]\frac{82}{10}+x=\frac{58}{5}[/tex][tex]x=\frac{58}{5}-\frac{82}{10}[/tex]Taking LCM of 5,10. LCM of 5,10 is 10
we get,
[tex]x=\frac{58\times2-82}{10}[/tex][tex]x=\frac{116-82}{10}[/tex][tex]x=\frac{34}{10}[/tex][tex]x=\frac{17}{5}[/tex][tex]x=3\frac{2}{5}[/tex]we get,
[tex]x=3\frac{2}{5}\text{ minutes}[/tex]Cindy takes 3 2/5 minutes.
2) To find the difference between fastest girl's time and slowest girl's time
Nicole is the fastest girl since her race time is 21/10 minutes
Cindy is the slowest girl with the race time 34/10 minutes
Difference between them is,
[tex]=\frac{34}{10}-\frac{21}{10}[/tex][tex]=\frac{13}{10}[/tex][tex]=1\frac{3}{10}\text{ minutes}[/tex]Difference is 1 3/10 minutes.
Answer is: 1 3/10 minutes.
