On a certain nonstop trip, Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours. What was her average speed in miles per hour for the entire trip?

To find Marta's average speed for the entire trip, we need to calculate the total distance and divide it by the total time. 1. Calculate the distance traveled at each speed: - Distance for the first 2 hours at x mph: 2x - Distance for the last 3 hours at y mph: 3y 2. Total distance: Total distance = 2x + 3y 3. Total time: Total time = 2 hours + 3 hours = 5 hours 4. Average speed (A): A = Total distance / Total time = (2x + 3y) / 5 Given the equations: i) 2x + 3y = 280 ii) y = x + 10 Substituting the second equation into the first: 2x + 3(x + 10) = 280 2x + 3x + 30 = 280 5x + 30 = 280 5x = 250 x = 50 Now find y: y = x + 10 = 50 + 10 = 60 Now substitute back into the average speed formula: Total distance = 2x + 3y = 2(50) + 3(60) = 100 + 180 = 280 Average speed: A = 280 / 5 = 56 miles per hour. Marta's average speed for the entire trip is 56 miles per hour.