# Suzie and Scott drive together for American freight. One day Suzie averaged 54 mph and Scott average 58mph, but Scott drove for 3 more hours than Suzie. If together they drove 734 miles, then for how many hours did Scott drive?

Sep 17, 2015

${t}_{2} = 8 h$

#### Explanation:

${v}_{1} = 54 m p h$
${v}_{2} = 58 m p h$
$\Delta t = 3 h$
${t}_{2} = {t}_{1} + \Delta t \implies {t}_{1} = t 2 - \Delta t$
$s = {s}_{1} + {s}_{2} = 734 m$
t_2=?

${s}_{1} = {v}_{1} \cdot {t}_{1}$
${s}_{2} = {v}_{2} \cdot {t}_{2}$
$s = {v}_{1} \cdot {t}_{1} + {v}_{2} \cdot {t}_{2}$
$s = {v}_{1} \cdot \left({t}_{2} - \Delta t\right) + {v}_{2} \cdot {t}_{2}$
$s = {v}_{1} \cdot {t}_{2} - {v}_{1} \cdot \Delta t + {v}_{2} \cdot {t}_{2}$
$s = {t}_{2} \cdot \left({v}_{1} + {v}_{2}\right) - {v}_{1} \cdot \Delta t$
${t}_{2} \cdot \left({v}_{1} + {v}_{2}\right) = s + {v}_{1} \cdot \Delta t$

${t}_{2} = \frac{s + {v}_{1} \cdot \Delta t}{{v}_{1} + {v}_{2}}$

${t}_{2} = \frac{734 m + 54 m p h \cdot 3 h}{54 m p h + 58 m p h} = \frac{734 m + 162 m}{112 m p h} = \frac{896 m}{112 m p h}$

${t}_{2} = 8 h$