SOLUTION: Robert can do a piece of work in "x" days. Mary can do the same work in (x+16) days. when both of them work together they can do work in 15 days. What is the value of "x"?

Question 135137: Robert can do a piece of work in "x" days. Mary can do the same work in (x+16) days. when both of them work together they can do work in 15 days. What is the value of "x"?
Found 2 solutions by ankor@dixie-net.com, scott8148:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Robert can do a piece of work in "x" days. Mary can do the same work in (x+16) days. when both of them work together they can do work in 15 days. What is the value of "x"?
:
Let "the piece of work" = 1
:
+ = 1
:
Multiply equation by x(x+16), results:
15(x+16) + 15x = x(x+16)
:
15x + 240 + 15x = x^2 + 16x
:
30x + 240 = x^2 + 16x
:
Arrange as a quadratic equation
x^2 + 16x - 30x - 240 = 0
:
x^2 - 14x - 240 = 0
Factors to:
(x-24)(x+10) = 0
:
x = +24 (ignore the negative solution)
;
:
Check solution
+ =
.625 + .375 = 1; confirms our solution
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
__ multiplying by x(x+16) __ 15x+240+15x=x^2+16x

subtracting 30x+240 __ 0=x^2-14x-240

factoring __ 0=(x-24)(x+10) __ x-24=0 and x+10=0

so, x=24
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