Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,600 nuts and 1,600 bolts? Pick:  A) 1,250 seconds  B) 1,500 seconds  C) 1,750 seconds  D) 2,400 seconds  E) 3,000 seconds
I used the Rate formula (R=\frac{1}{T})   Rate of 1st machine = Rate of making 1 bolt + Rate of making 1 nut = 1 + \frac{1}{2}   Rate of 1st machine = Rate of 2nd machine   After this I got lost.   Please can you help how to approach using algebra?   I wouldn't complicate:   1 machine needs 1,600*1 seconds to produce 1,600 bolts, so 2 need half of that, so 1,600/2 seconds.=800   1 machine needs 1,600*2 seconds to produce 1,600 nuts, so 2 need half of that, so 1,600*2/2 seconds.=1600   total = 2400   2,400 seconds
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Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 1,600 nuts and 1,600 bolts?