Let Janet's speed be x
Bonnie's speed would be 5 + x
The time for Bonnie to travel 60 miles is
[tex]\frac{dis\tan ce}{\text{speed}}=\frac{60}{5+x}[/tex]The time for Janet to travel 75 miles is
[tex]\frac{75}{x}[/tex]Thus we have from the information
[tex]\begin{gathered} \frac{60}{5+x}=\frac{75}{x}-1 \\ \frac{60}{5+x}=\text{ }\frac{75-x}{x} \\ \end{gathered}[/tex]Cross multiply
[tex]\begin{gathered} 60x=(5+x)(75-x) \\ 60x=375-5x-x^2+75x \\ x^2-10x-375=0 \end{gathered}[/tex]Solving this quadratic equation for x, we have
[tex]\begin{gathered} x^2-25x+15x-375=0 \\ x(x-25)+15(x-25)=0 \\ (x+15)(x-25)=0 \end{gathered}[/tex]Thus x = -15 or 25.
The speed cannot be a negative number, so x = 25
Therefore Bonnie's speed = 25 miles per hour
and Janet's speed = 25 - 5 = 20 miles per hour
