SOLUTION: Suppose that y varies directly as w and inversely as t. If y=4 when w=1/4 and t=1/2, find y when w=2 and t=16

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Question 835038: Suppose that y varies directly as w and inversely as t.
If y=4 when w=1/4 and t=1/2, find y when w=2 and t=16
Found 2 solutions by Theo, stanbon:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
if y varies directly as w, then the equation would be y = kw
if y varies inversely with t, then the equation would be y = k/t
since y varies directly with w and inversely with t at the same time, the equation becomes y = kw/t.
if y = 4 when w = 1/4 and t = 1/2, you can use this equation to find the value of k.
your equation becomes 4 = (k * (1/4) / (1/2)
since a division by 1/2 is the same as a multiplication by 2, the equation simplifies to:
4 = (1/4) * k * 2
simplify this to get:
4 = 2/4 * k which further simplifies to 4 = 1/2 * k
multiply both sides of this equation by 2 and you get:
8 = k
the value of k should be equal to 8.
you can test by substituting k in the original equation.
the original equation says that 4 = (1/4) * k / (1/2)
replace k with 8 in this equation to get:
4 = (1/4) * 8 / (1/2)
simplify to get:
4 = 2 / (1/2)
simplify further to get 4 = 4 confirming that k = 8 is correct.
now that you know k, you can use it to solve the second part of your problem.
that second part says:
find y when w = 2 and t = 16
the equation is still y = k * w / t
replace all variables with their known values and you get:
y = 8 * 2 / 16 which results in y = 16 / 16 which results in y = 1.
see the following link for an online explanation of the combined variation equation used in this problelm.
http://hotmath.com/hotmath_help/topics/combined-variation.html

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Suppose that y varies directly as w and inversely as t.
y = kw/t
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Solve for "k" using "y=4 when w=1/4 and t=1/2"
1/2 = k*(1/4)/4
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k = 2/(1/4) = 8
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Equation: y = 8*w/t
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Find y when w=2 and t=16
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y = 8*2/16 = 1
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Cheers,
Stan H.
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