We have that Lin ran
[tex]2\frac{3}{4}=\frac{11}{4}[/tex]11/4 miles in 2/5 hours. So we have that the rate is
[tex]\frac{\frac{11}{4}}{\frac{2}{5}}=\frac{55}{8}[/tex]55/8 miles per hour
if we want to know the time she would need to run 10 miles we have to divide 10 by the rate
[tex]\frac{10}{\frac{55}{8}}=\frac{80}{55}=\frac{16}{11}=1\frac{5}{11}hours[/tex]