Question

HELP?!?!




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

Answer 1

Yes, let y = 51.5-x and substitute it into the second equation, then solve for x.

Answer 2

I got it, x=22, y=26.4

Answer 3

Well, your x + y here does not equal 51.5. Try again.

Answer 4

It accepted that answer. I got it figured out.

Answer 5

I see. It accepted C, because you had the right x and the other value was not y, but where the rate changed.

Answer 6

Oh, I don't know, I don't really understand where I went wrong when I originally got D. as the answer...

Answer 7

Once you found x, the time of the first part, then the height of the first part was her speed times that time....

Answer 8

Oh, so you just input x into where you supplimented it to get y then?

Answer 9

Yes, you get y from x. Unfortunately, I misread the question a bit and thought x was the time for the lower part, when y was. You figured it out, though. Sorry.