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Answer :
Sure! Let's solve each part of the question step-by-step.
1. How many machines will you need to produce 500 items per hour?
- We know each machine produces 100 items in one hour.
- To find out how many machines we need to produce 500 items, we divide 500 items by the rate of 100 items per machine.
- Calculation: [tex]\( \frac{500}{100} = 5 \)[/tex].
- Therefore, we need 5 machines to produce 500 items per hour.
2. How long will it take 4 machines to produce 100 items?
- Each machine produces 100 items in one hour. So, 4 machines working together will produce 4 times that amount in the same time.
- Total production by 4 machines in one hour: [tex]\( 4 \times 100 = 400 \)[/tex] items.
- To find how long it will take to produce 100 items, we divide 100 items by the production rate of 400 items per hour.
- Calculation: [tex]\( \frac{100}{400} = 0.25 \)[/tex] hours.
- Therefore, it will take 0.25 hours, or 15 minutes, for 4 machines to produce 100 items.
3. How many items do 8 machines produce in 45 minutes?
- First, determine how many items 8 machines produce in one hour:
- Production by one machine in one hour is 100 items.
- Total for 8 machines: [tex]\( 8 \times 100 = 800 \)[/tex] items per hour.
- Since we need the output in 45 minutes, which is three-quarters of an hour, we calculate:
- Calculation: [tex]\( \frac{45}{60} \times 800 = 0.75 \times 800 = 600 \)[/tex].
- Therefore, 8 machines produce 600 items in 45 minutes.
4. If a rescue vessel has enough provisions for 10 people to survive for 6 days, how long will 12 people survive on the vessel?
- Initially, the total provision is enough for 10 people for 6 days: [tex]\( 10 \times 6 = 60 \)[/tex] person-days.
- Now, we need to find out for how many days these provisions will last for 12 people.
- Calculation: [tex]\( \frac{60}{12} = 5 \)[/tex] days.
- Therefore, 12 people will survive for 5 days on the vessel with the given provisions.
These calculations provide a clear understanding of the solutions to each question.
1. How many machines will you need to produce 500 items per hour?
- We know each machine produces 100 items in one hour.
- To find out how many machines we need to produce 500 items, we divide 500 items by the rate of 100 items per machine.
- Calculation: [tex]\( \frac{500}{100} = 5 \)[/tex].
- Therefore, we need 5 machines to produce 500 items per hour.
2. How long will it take 4 machines to produce 100 items?
- Each machine produces 100 items in one hour. So, 4 machines working together will produce 4 times that amount in the same time.
- Total production by 4 machines in one hour: [tex]\( 4 \times 100 = 400 \)[/tex] items.
- To find how long it will take to produce 100 items, we divide 100 items by the production rate of 400 items per hour.
- Calculation: [tex]\( \frac{100}{400} = 0.25 \)[/tex] hours.
- Therefore, it will take 0.25 hours, or 15 minutes, for 4 machines to produce 100 items.
3. How many items do 8 machines produce in 45 minutes?
- First, determine how many items 8 machines produce in one hour:
- Production by one machine in one hour is 100 items.
- Total for 8 machines: [tex]\( 8 \times 100 = 800 \)[/tex] items per hour.
- Since we need the output in 45 minutes, which is three-quarters of an hour, we calculate:
- Calculation: [tex]\( \frac{45}{60} \times 800 = 0.75 \times 800 = 600 \)[/tex].
- Therefore, 8 machines produce 600 items in 45 minutes.
4. If a rescue vessel has enough provisions for 10 people to survive for 6 days, how long will 12 people survive on the vessel?
- Initially, the total provision is enough for 10 people for 6 days: [tex]\( 10 \times 6 = 60 \)[/tex] person-days.
- Now, we need to find out for how many days these provisions will last for 12 people.
- Calculation: [tex]\( \frac{60}{12} = 5 \)[/tex] days.
- Therefore, 12 people will survive for 5 days on the vessel with the given provisions.
These calculations provide a clear understanding of the solutions to each question.
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