Rates are ADDITIVE:
X's rate + Y's rate = combined rate for X and Y
Rate formula:
\(rate = \frac{work}{time}\)
TalonShade wrote:
Maybe its a super ignorant doubt but what am I doing wrong if I do the following -
If Y does W work - its rate is 1/W so the other one is 1/(W+2)
Giving us
1/W + 1/(W+2) = 5W/12
Not sure why this is throwing me off
Here, \(w\) represents the amount of work, so it does not belong in the denominator.
Let the job = w = 1 widget
Let X's time = x
Since X takes x days to produce 1 widget, we get:
X's rate \(= \frac{work}{time} = \frac{1}{x}\)
Since Y takes 2 fewer days to produce 1 widget, we get:
Y's rate = \(\frac{work}{time} = \frac{1}{x-2}\)
Since X and Y together take 3 days to produce 5/4 of 1 widget, we get:
Combined rate for X and Y \(= \frac{work}{time} = \frac{5}{4} ÷ 3 = \frac{5}{12}\)
Since X's rate + Y's rate = combined rate for X and Y, we get:
\(\frac{1}{x} + \frac{1}{x-2} = \frac{5}{12}\)
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