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? a) lower ascent in 25 min; rate changed at 30 feet
b) lower ascent in 22 min; rate changed at 26.4 feet
c) lower ascent in 23.5 min; rate changed at 28.2 feet
d) lower ascent in 9.5 min; rate changed at 9.7 feet

Answer 1

If x is the length of the "lower" wall in feet and y = length of "upper" wall in feet, we know that the sum of the lengths of the lower and upper wall need to add up to the total length of 50 feet so
\[x+y=50\]

Answer 2

We know that the climber took 1.2 ft/min to climb the lower length x and 0.8 ft/min to climb the upper length of y feet and the whole thing took 51.5 min. so:\[1.2x +0.8y =51.5\]

Answer 3

Solve the first equation for y and substitute into the second equation.