Let t=time Doreen travels; let r=rate of Doreen
RATE TIME = DIST.
Sue | r+13 t-3 105
Doreen | r t 64
Now solve the system:
(r+13)(t-3)=105
rt=64
\(r= \frac{64}{t}
\\
\\(\frac{64}{t} +13)(t-3)=105
\\
\\64- \frac{192} {t}+13t-39-105=0
\\
\\13t- \frac{192} {t}-80=0
\\
\\ 13t^2-80t-192=0
\\
\\t_{1,2}= \frac{80\pm \sqrt{(-80)^2-4\times13(-192)} }{2\times13}= \frac{80\pm128}{26}
\\
\\t=\frac{80+128}{26} =8
\\
\\r=\frac{64}{t} =\frac{64}{8} =8\)
Doreen: rate = 8 mph, time = 8 hours
Sue: rate = 21 mph, time = 5 hours