Machine X produces W widgets in five minutes Machine X and Y

Machine X produces W widgets in five minutes. Machine X and Y, working at the same time, produce W widgets in two minutes. How long will it take Machine Y, working alone to produce W widgets?

Solution

Machine X produces W widgets in five minutes.
X-DATA:
time = 5 min/job ; rate = 1/5 job/min
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Machine X and Y, working at the same time, produce W widgets in two minutes.
Together DATA:
time = 2 min/job ; rate = 1/2 job/min
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How long will it take Machine Y, working alone to produce W widgets?
Y-DATA:
time = k min/job ; rate = 1/k job/min
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Equation:
rate + rate = together rate
1/5 + 1/k = 1/2
Multiply thru by 10k to get:
2k + 10 = 5k
3k = 10
k = 3 1/3 min (time it would take Machine Y to produce W widgets)