jmc

Question

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 22 miles. The second and third days she averaged 13 miles per day. The last two days she hiked a total of 30 miles. The total hike for the first and third days was 26 miles. How many miles long was the trail?

Accepted Answer

Let the number of miles Phoenix hiked in each day be a, b, c, and d. We have the equations align* a+b&=22 (b+c)/2=13 b+c&=26 c+d&=30 a+c&=26 align* Notice that we do not have to solve for any of the variables. We can add a + b = 22 to c + d = 30 and find that a + b + c + d = 11 + 11 + 15 + 15 = 52. Therefore, the entire trail was 52 miles long.