ect the correct answerA factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 500 nuts per minute and need to be cleared for 10 minutes after production of 2000 nuts. The machine producing only bolts produces 600 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts. Find the minimum time required to produce 6000 pairs of bolts and nuts if both machines are operated simultaneously?Options32 minutes25 minutes20 minutes40 minutes
Question
ect the correct answerA factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 500 nuts per minute and need to be cleared for 10 minutes after production of 2000 nuts. The machine producing only bolts produces 600 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts. Find the minimum time required to produce 6000 pairs of bolts and nuts if both machines are operated simultaneously?Options32 minutes25 minutes20 minutes40 minutes
Solution
To solve this problem, we need to calculate the time it takes for each machine to produce the required number of nuts and bolts, including the time it takes to clear the machines.
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For the nuts: The machine produces 500 nuts per minute and needs to be cleared for 10 minutes after producing 2000 nuts. To produce 6000 nuts, the machine will need to be cleared 3 times (6000/2000 = 3). The time to produce 6000 nuts is 6000/500 = 12 minutes. The total time to produce 6000 nuts, including clearing, is 12 minutes + 3*10 minutes = 42 minutes.
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For the bolts: The machine produces 600 bolts per minute and needs to be cleared for 15 minutes after producing 3000 bolts. To produce 6000 bolts, the machine will need to be cleared 2 times (6000/3000 = 2). The time to produce 6000 bolts is 6000/600 = 10 minutes. The total time to produce 6000 bolts, including clearing, is 10 minutes + 2*15 minutes = 40 minutes.
Since both machines are operated simultaneously, the minimum time required to produce 6000 pairs of bolts and nuts is the maximum of the two times calculated, which is 42 minutes. However, this option is not available in the given options. There might be a mistake in the problem or the options provided.
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