



 
Hi Ruby, Here is my diagram of Amy's trip. She drove from her home $H$ to grandma's house $H$ on a direct fast route. In the afternoon she drove home on local roads, a more indirect route. Suppose the distance she travelled to grandma's house was $d_1$ miles and it took her $t_1$ hours, and the distance she travelled from grandma's house to home was $d_2$ miles and it took her $t_2$ hours. What facts do you know? The total distance she travelled was 300 miles so \[d_1 + d_2 = 300 \mbox{ miles.}\] She spent $t_1 + t_2$ hours driving and 2 hours at grandma's house and her total time was 8 hours. Thus \[t_1 + t_2 + 2 = 8 \mbox{ hours.}\] On the trip to grandma's house she drove $d_1$ miles in $t_1$ hours and her speed was 70 miles per hour so \[70 = \frac{d_1}{t_1} \mbox{ or } 70 \times t_1 = d_{1}.\] Likewise for the return trip we get \[40 \times t_2 = d_{2}.\] I would suggest that you solve the first equation for $d_1$ and the second equation for $t_1$ and substitute these values into the third equation. This converts the third equation to one involving $d_2$ and $t_{2}.$ The fourth equation also involves $d_2$ and $t_{2}.$ Solve these two equations for $d_2$ and $t_{2}.$ Penny 



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