Question 930639
x = time eric alone takes to paint
y = time ryan alone takes to paint = 6 hours
z = time eric and ryan together take to paint = (2/3)x
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r = w/t
rates are additive:
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eric rate = 1/x
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ryan rate = 1/6
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together rate:
1/x + 1/6 = 1/z
1/x + 1/6 = 1/(2/3)x
1/x - 1/(2/3)x = -1/6
(2/3)/(2/3)x - 1/(2/3)x = -1/6
(2/3) - 1 = (-1/6)*(2/3)x
(2/3) - (3/3) = (-1/6)*(2/3)x
-(1/3) = (-1/6)*(2/3)x
x = -(1/3)/( (-1/6)*(2/3) )
x = 3
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answer:
x = time eric alone takes to paint = 3 hours
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