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Bunuel
Machine A produces nails at a uniform rate of 120 every 10 seconds, and Machine B produces nails at a uniform rate of 100 every 15 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 140 nails?

A. 7.0
B. 7.5
C. 8.0
D. 8.5
E. 9.0

Given: Machine A produces nails at a uniform rate of 120 every 10 seconds, and Machine B produces nails at a uniform rate of 100 every 15 seconds.

Asked: If the two machines run simultaneously, how many seconds will it take for them to produce a total of 140 nails?


Machine A produces nails = 120/10 = 12 nails/second

Machine B produces nails = 100/15 = 20/3 = 6 2/3 nails/second

Machine A & Machine B produces nails = 12 + 6 2/3 = 18 2/3 = 56/3 nails/second

Time taken to produce total of 140 nails = \(\frac{140}{\frac{56}{3}}\) =7.5 seconds

IMO B
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Bunuel
Machine A produces nails at a uniform rate of 120 every 10 seconds, and Machine B produces nails at a uniform rate of 100 every 15 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 140 nails?

A. 7.0
B. 7.5
C. 8.0
D. 8.5
E. 9.0
Efficiency of machine A is 120/10 = 12
Efficiency of machine B is 100/15 = 20/3

Combined efficiency of Machine A and B is 36 + 20/3 =56/3

Time required to produce 140 nails is 140*3/56 = 10*3/4 = 7.5, Answer must be (B)
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