In a lock and key factory, the locks machine produces 100 locks per hour and needs to be oiled for 5 hours for every 1000 locks produced. The keys machine produces 150 keys per hour and needs oiling for 10 hours after production of every 3000 keys. If both machines start at the same time, what is the minimum duration (in hours) required for producing 6000 sets, each set comprising one lock and two keys?12011096100
Question
In a lock and key factory, the locks machine produces 100 locks per hour and needs to be oiled for 5 hours for every 1000 locks produced. The keys machine produces 150 keys per hour and needs oiling for 10 hours after production of every 3000 keys. If both machines start at the same time, what is the minimum duration (in hours) required for producing 6000 sets, each set comprising one lock and two keys?12011096100
Solution
To solve this problem, we need to calculate the time taken by each machine to produce the required number of locks and keys, and then take the maximum of these times as both machines work simultaneously.
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Calculate the time taken to produce locks:
- The lock machine produces 100 locks per hour.
- For 6000 locks (since 1 set contains 1 lock), it would take 6000/100 = 60 hours.
- Additionally, the machine needs to be oiled for 5 hours for every 1000 locks produced. So for 6000 locks, it would need to be oiled for 5*6 = 30 hours.
- Therefore, total time taken to produce 6000 locks is 60 + 30 = 90 hours.
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Calculate the time taken to produce keys:
- The key machine produces 150 keys per hour.
- For 12000 keys (since 1 set contains 2 keys), it would take 12000/150 = 80 hours.
- Additionally, the machine needs to be oiled for 10 hours for every 3000 keys produced. So for 12000 keys, it would need to be oiled for 10*4 = 40 hours.
- Therefore, total time taken to produce 12000 keys is 80 + 40 = 120 hours.
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Since both machines work simultaneously, the minimum duration required for producing 6000 sets is the maximum of the times calculated above, which is 120 hours.
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