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?

dolphinia Aug 27, 2023

#1**0 **

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.

Guest Aug 27, 2023