Julie drives 100 mi to Grandmother's house. On the way to Grandmother's, Julie drives half the distance at 33.0 and half the distance at 80.0 . On her return trip, she drives half the time at 33.0 and half the time at 80.0 . What is Julie's average speed on the way to Grandmother's house? What is her average speed on the return trip?

Question

Julie drives 100 mi to Grandmother's house. On the way to Grandmother's, Julie drives half the distance at 33.0  and half the distance at 80.0 . On her return trip, she drives half the time at 33.0  and half the time at 80.0 . What is Julie's average speed on the way to Grandmother's house? What is her average speed on the return trip?

anonymous · Answer

$$t=\frac{d}{r},r=\frac{d}{t}  $$$$\frac{100}{\frac{50}{33}+\frac{50}{80}}=\frac{5280}{113}=46.7 \text{ mph}$$Let t be the total time for the return trip from Grandma's house:$$r t = d$$Solve the following for t:$$33 \frac{t}{2}+80\frac{t}{2}= 100$$$$t=\frac{200}{113} $$$$\frac{100}{\left(\frac{200}{113}\right)}=\frac{113}{2}=56.5 \text{mph} $$