SOLUTION: Height and Weight Suppose that the weight of a person is directly proportional to the cube of the person’s height. If one person weighs twice as much as a (similarly proportione

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Height and Weight Suppose that the weight of a person is directly proportional to the cube of the person’s height. If one person weighs twice as much as a (similarly proportione      Log On


   

Question 424085: Height and Weight Suppose that the weight of a
person is directly proportional to the cube of the
person’s height. If one person weighs twice as much
as a (similarly proportioned) second person, by what
factor is the heavier person’s height greater than the
shorter person’s height?
Found 2 solutions by mananth, stanbon:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
w= h1^3........ person a
2w= h2^3
h2^3/h1^3= 2w/w
h2/h1= cubroot 2

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Height and Weight
---------------------------------
Suppose that the weight of a
person is directly proportional to the cube of the
person’s height.
--
W = k*H^3
----------------------------------------
If one person weighs twice as much
as a (similarly proportioned) second person, by what
factor is the heavier person’s height greater than the
shorter person’s height?
--
Let the 2nd person's weight be "x"
x = k*H^3
H = [x/k]^(1/3) (2nd person's height)
-------------------
The 1st person's weight is "2x"
2x = kH^3
H = [2x/k]^(1/3)
H = 2^(1/3)[x/k]^(1/3) (1st person's height)
-----
By what factor is the heavier person’s height greater than the
shorter person’s height?
Answer: 2^(1/3)
=========================
Cheers,
Stan H.
================