Question

Anyone good at story problems.. i could really use some help. thanks ahead.

Answer 1

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.)

Answer 2

If you could help that would be great :)

Answer 3

Are there any multiple choice answers?

Answer 4

Yes Im bringing them up.. hhold a sec thanks :)

Answer 5

22 minutes.
I'm working on the justification.

Answer 6

Give me a min

Answer 7

Thanks @LovelyAnna

Answer 8

I would say the first one, lower ascent in 23.5 min; rate changed at 28.2 feet

Answer 9

My bad.. I meant: lower ascent in 22 min; rate changed at 26.4 feet

Answer 10

Okay thanks :) could you explain how you figure that?

Answer 11

Sure, give me another min!

Answer 12

:) okay

Answer 13

Refer to the Mathematica attachment.

Answer 14

[(0.8 ft/min) * (X min)] + [(1.2 ft/min) * (51.4 -X) min] = 50 feet (cancel terms)
(0.8 ft)X + [(1.2 ft)(51.4) - (1.2 ft)X = 50 feet (combine values)
(0.8 ft - 1.2 ft)X = 50 ft - 61.68 ft
(-0.4 ft)X = -11.68 ft
X = -11.68 ft/-0.4 ft
X= 29.2
(22.2 min)
[(0.8 ft/min)(29.2 min)] + [(1.2 ft/min)(51.4-29.2 min)] = 50 ft (replace X in original equation)

23.36 ft + 26.64 ft = 50 feet

Therefor, lower assent in 22 minutes, rate changed at 26.4 feet

Hope this helped!

Answer 15

Yes that did thanks!!

Answer 16

@robtobey thanks for the pdf :)

Answer 17

You are welcome.