+1306 Phoenix hiked the Rocky Path Trail last week. It took four days to complete the trip. The first two days she hiked a total of 26 miles. The second and third days she averaged 12 miles per day. The last two days she hiked a total of miles. The total hike for the first and third days was 22 miles. How many miles long was the trail?
Let d1, d2, d3, and d4 be the number of miles Phoenix hiked on days 1, 2, 3, and 4, respectively. We are given the following system of equations:
\begin{align*} d_1 + d_2 &= 26 \ d_2 + d_3 &= 24 \ d_3 + d_4 &= 22 \ d_1 + d_3 &= 22 \end{align*}Subtracting the second and third equations, we get d1−d4=2. Substituting this into the fourth equation, we get 2+d4=22, so d4=20. Substituting this into the third equation, we get d3+20=22, so d3=2. Substituting this into the second equation, we get d2+2=24, so d2=22. Substituting the values of d2 and d3 into the first equation, we get d1+22=26, so d1=4.
Therefore, Phoenix hiked a total of d1+d2+d3+d4=4+22+2+20=48 miles on the Rocky Path Trail.
