Answer :
Sure, let's break down the solution step by step for each part of the question:
1. How many machines will you need to produce 500 items per hour?
- If one machine produces 100 items in one hour, to find out how many machines are needed to produce 500 items in one hour, you divide the total target items (500) by the number of items one machine can produce in an hour (100).
- Calculation: [tex]\( \frac{500 \text{ items}}{100 \text{ items/machine/hour}} = 5 \)[/tex]
- So, you will need 5 machines to produce 500 items per hour.
2. How long will it take 4 machines to produce 100 items?
- If one machine produces 100 items in one hour, then 4 machines working together will produce [tex]\( 4 \times 100 = 400 \)[/tex] items in one hour.
- To produce 100 items with these 4 machines, you'd divide the target items (100) by the rate of 400 items per hour.
- Calculation: [tex]\( \frac{100 \text{ items}}{400 \text{ items/hour}} = 0.25 \text{ hours} \)[/tex]
- Therefore, it will take 4 machines 0.25 hours, which is 15 minutes, to produce 100 items.
3. How many items do 8 machines produce in 45 minutes?
- One machine produces 100 items per hour, so 8 machines will produce [tex]\( 8 \times 100 = 800 \)[/tex] items in one hour.
- Since 45 minutes is 0.75 hours (because 45 minutes divided by 60 minutes is 0.75), you multiply the production rate by this time.
- Calculation: [tex]\( 800 \text{ items/hour} \times 0.75 \text{ hours} = 600 \text{ items} \)[/tex]
- So, 8 machines will 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?
- If 10 people can survive for 6 days, the total person-days of provisions available can be calculated by multiplying the number of people by the number of days: [tex]\( 10 \times 6 = 60 \)[/tex] person-days.
- To find out how long 12 people can survive on these provisions, divide the total person-days by the number of people: [tex]\( \frac{60 \text{ person-days}}{12 \text{ people}} = 5 \)[/tex] days.
- Thus, 12 people will survive for 5 days on the vessel.
I hope this helps clarify the solution for each part of the question!
1. How many machines will you need to produce 500 items per hour?
- If one machine produces 100 items in one hour, to find out how many machines are needed to produce 500 items in one hour, you divide the total target items (500) by the number of items one machine can produce in an hour (100).
- Calculation: [tex]\( \frac{500 \text{ items}}{100 \text{ items/machine/hour}} = 5 \)[/tex]
- So, you will need 5 machines to produce 500 items per hour.
2. How long will it take 4 machines to produce 100 items?
- If one machine produces 100 items in one hour, then 4 machines working together will produce [tex]\( 4 \times 100 = 400 \)[/tex] items in one hour.
- To produce 100 items with these 4 machines, you'd divide the target items (100) by the rate of 400 items per hour.
- Calculation: [tex]\( \frac{100 \text{ items}}{400 \text{ items/hour}} = 0.25 \text{ hours} \)[/tex]
- Therefore, it will take 4 machines 0.25 hours, which is 15 minutes, to produce 100 items.
3. How many items do 8 machines produce in 45 minutes?
- One machine produces 100 items per hour, so 8 machines will produce [tex]\( 8 \times 100 = 800 \)[/tex] items in one hour.
- Since 45 minutes is 0.75 hours (because 45 minutes divided by 60 minutes is 0.75), you multiply the production rate by this time.
- Calculation: [tex]\( 800 \text{ items/hour} \times 0.75 \text{ hours} = 600 \text{ items} \)[/tex]
- So, 8 machines will 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?
- If 10 people can survive for 6 days, the total person-days of provisions available can be calculated by multiplying the number of people by the number of days: [tex]\( 10 \times 6 = 60 \)[/tex] person-days.
- To find out how long 12 people can survive on these provisions, divide the total person-days by the number of people: [tex]\( \frac{60 \text{ person-days}}{12 \text{ people}} = 5 \)[/tex] days.
- Thus, 12 people will survive for 5 days on the vessel.
I hope this helps clarify the solution for each part of the question!
