Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets? 答案为12
In a work problem, the rates at which certain persons or machines work alone are usually given, and it is necessary to compute the rate at which they work together.
The basic formula for solving work problems is 1/r+1/s=1/h,where r and s are, for example, the number of hours it takes Rae and Sam, respectively, to complete a job when working alone, and h is nubmber of hours it takes Rae and Sam when working together.
In this case, 3 is the number of hours X and Y work together. 5/4 is the output of work taking the two 3 day to finish. According to the formula "1/r+1/s=1/h", here r=t, s=t+2, h=3. "1" in "1/h" is replaced by "5/4".
category X Y (X + Y) make w d + 2 d make 5w/4 ? 3 Rate w/(d +2) w/d 5w/12
Since the combined rate of (X + Y) equals the combination of each individual rate, then [w/(d +2) + w/d] = 5w/12 or [d + (d + 2)]*12 = 5 * d * (d + 2). So d = 4 To make 2w, X alone will take = [2w] / [w/6] = 12 days
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发表于 2010-12-24 17:46:03
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