Question

A climber goes up the lower part of a 50-foot climbing wall at a rate of 1.2 ft/min. The upper part of the wall is more difficult, and she climbs at 0.8 ft/min. She reaches the top of the wall in 51.5 min. How long did it take her to climb the lower part of the wall? At what height on the wall did her rate change? (Hint: Model each part of the climb with a linear equation, using x for the time and y for distance. Then solve the system of two linear equations for x and y.)

My teacher told me "Let x be the number of minutes for the upper part. Your equations are x + y = 51.5 and 1.2x + 0.8y =50. Use substitution to solve for both variables."

A. lower ascent in 9.5 min; rate changed at 9.7 feet
B. lower ascent in 25 min; rate changed at 30 feet
C. lower ascent in 22 min; rate changed at 26.4 feet
D. lower ascent in 23.5 min; rate changed at 28.2 feet