Answer :
Sure! Let's solve the questions step by step:
1. How many machines will you need to produce 500 items per hour?
- Each machine produces 100 items in one hour.
- To find out how many machines are needed to produce 500 items per hour, you can divide the target number of items (500) by the number of items one machine can produce in an hour (100).
- Calculation: [tex]\( \frac{500}{100} = 5 \)[/tex]
- You will 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.
- If you have 4 machines, they will collectively produce [tex]\(4 \times 100 = 400\)[/tex] items in one hour.
- To find out how long it takes to produce 100 items, divide the target number of items (100) by the number of items produced by 4 machines in one hour (400).
- Calculation: [tex]\( \frac{100}{400} = 0.25 \)[/tex] hours
- To convert hours to minutes, multiply by 60.
- Calculation: [tex]\(0.25 \times 60 = 15\)[/tex] minutes
- It will take 4 machines 15 minutes to produce 100 items.
3. How many items do 8 machines produce in 45 minutes?
- Each machine produces 100 items in one hour.
- With 8 machines, they can collectively produce [tex]\(8 \times 100 = 800\)[/tex] items in one hour.
- First, convert 45 minutes into hours: [tex]\( \frac{45}{60} = 0.75 \)[/tex] hours.
- To find out how many items are produced in 45 minutes, multiply the production rate per hour by the time in hours.
- Calculation: [tex]\(800 \times 0.75 = 600\)[/tex]
- 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?
- Initially, 10 people can survive for 6 days, meaning the provisions are enough for [tex]\(10 \times 6 = 60\)[/tex] person-days.
- To find out how many days 12 people can survive, divide the total person-days by the number of people.
- Calculation: [tex]\( \frac{60}{12} = 5\)[/tex] days
- 12 people will survive for 5 days on the vessel with the given provisions.
I hope this step-by-step explanation helps you understand how to approach and solve these types of problems!
1. How many machines will you need to produce 500 items per hour?
- Each machine produces 100 items in one hour.
- To find out how many machines are needed to produce 500 items per hour, you can divide the target number of items (500) by the number of items one machine can produce in an hour (100).
- Calculation: [tex]\( \frac{500}{100} = 5 \)[/tex]
- You will 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.
- If you have 4 machines, they will collectively produce [tex]\(4 \times 100 = 400\)[/tex] items in one hour.
- To find out how long it takes to produce 100 items, divide the target number of items (100) by the number of items produced by 4 machines in one hour (400).
- Calculation: [tex]\( \frac{100}{400} = 0.25 \)[/tex] hours
- To convert hours to minutes, multiply by 60.
- Calculation: [tex]\(0.25 \times 60 = 15\)[/tex] minutes
- It will take 4 machines 15 minutes to produce 100 items.
3. How many items do 8 machines produce in 45 minutes?
- Each machine produces 100 items in one hour.
- With 8 machines, they can collectively produce [tex]\(8 \times 100 = 800\)[/tex] items in one hour.
- First, convert 45 minutes into hours: [tex]\( \frac{45}{60} = 0.75 \)[/tex] hours.
- To find out how many items are produced in 45 minutes, multiply the production rate per hour by the time in hours.
- Calculation: [tex]\(800 \times 0.75 = 600\)[/tex]
- 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?
- Initially, 10 people can survive for 6 days, meaning the provisions are enough for [tex]\(10 \times 6 = 60\)[/tex] person-days.
- To find out how many days 12 people can survive, divide the total person-days by the number of people.
- Calculation: [tex]\( \frac{60}{12} = 5\)[/tex] days
- 12 people will survive for 5 days on the vessel with the given provisions.
I hope this step-by-step explanation helps you understand how to approach and solve these types of problems!
