SOLUTION: I have a story problem I can't figure out. Can you help me and show me the steps to solve it? Thanks you. The speed of a moving walkway is about 4.5 feet per second. Walking on the

Algebra ->  College  -> Linear Algebra -> SOLUTION: I have a story problem I can't figure out. Can you help me and show me the steps to solve it? Thanks you. The speed of a moving walkway is about 4.5 feet per second. Walking on the      Log On


   

Question 485104: I have a story problem I can't figure out. Can you help me and show me the steps to solve it? Thanks you. The speed of a moving walkway is about 4.5 feet per second. Walking on the moving walkway, it takes Karen a total of 20 seconds to travel 45 feet with the movement of the walkway and then back again against the movement of the walkway. What is Karen's normal walking speed?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The speed of a moving walkway is about 4.5 feet per second.
Walking on the moving walkway, it takes Karen a total of 20 seconds to travel 45
feet with the movement of the walkway and then back again against the movement of the walkway.
What is Karen's normal walking speed?
:
Let x = K's normal walking speed in ft/sec
then
(x+4.5) = K's speed going the same as the walkway
and
(x-4.5) = K's speed going against the walkway
:
Write a time equation: time = dist/speed
:
with time + against time = 20 sec
45%2F%28x%2B4.5%29 + 45%2F%28x-4.5%29 = 20
:
Multiply by (x+4.5)(x-4.5)
(x+4.5)(x-4.5)*45%2F%28x%2B4.5%29 + (x+4.5)(x-4.5)*45%2F%28x-4.5%29 = 20(x+4.5)(x-4.5)
:
Cancel the denominators FOIL the right side and you have:
45(x-4.5) + 45(x+4.5) = 20(x^2 - 4.5x + 4.5x - 20.25)
:
45x - 202.5 + 45x + 202.5 = 20(x^2 - 20.25)
:
90x = 20x^2 - 405
A quadratic equation
20x^2 - 90x - 405 = 0
Simplify, divide by 5
4x^2 - 18x - 81 = 0
Use the quadratic formula to find x
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=4; b=-18; c=-81
x+=+%28-%28-18%29+%2B-+sqrt%28-18%5E2-4%2A4%2A-81+%29%29%2F%282%2A4%29+
:
x+=+%2818+%2B-+sqrt%28324-%28-1296%29+%29%29%2F%288%29+
:
x+=+%2818+%2B-+sqrt%281620+%29%29%2F%288%29+
we only care about the positive solution here
x+=+%2818+%2B+40.25%29%2F%288%29+
x = 58.25%2F8
x = 7.28 ft/sec is K's normal walking speed
:
:
You can confirm this by finding the time for each direction:
45/(7.28+4.5) = 3.82 sec
45/(7.28-4.5) = 16.18 sec
---------------------------
round trip time:20.00 sec
:
Did you understand the steps we took here?