Answer :
Sure! Let's break down each of 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 produce 500 items in one hour, you need several machines.
- Divide the target number of items (500) by the number of items one machine produces (100).
- [tex]\( \text{Number of machines needed} = \frac{500}{100} = 5 \)[/tex].
- So, you need 5 machines.
2. How long will it take 4 machines to produce 100 items?
- Each machine produces 100 items in one hour.
- Four machines combined produce [tex]\( 4 \times 100 = 400 \)[/tex] items in one hour.
- You need to produce 100 items.
- Divide the target number of items (100) by the total number of items produced by 4 machines in one hour (400).
- [tex]\( \text{Time required in hours} = \frac{100}{400} = 0.25 \)[/tex].
- So, it will take 0.25 hours, which is 15 minutes.
3. How many items do 8 machines produce in 45 minutes?
- Each machine produces 100 items in one hour.
- Eight machines produce [tex]\( 8 \times 100 = 800 \)[/tex] items in one hour.
- Convert 45 minutes to hours [tex]\( \text{(45 minutes)} = \frac{45}{60} \)[/tex] hours = 0.75 hours.
- Multiply the number of items produced by 8 machines in one hour by 0.75.
- [tex]\( \text{Items produced} = 800 \times 0.75 = 600 \)[/tex].
- So, 8 machines produce 600 items in 45 minutes.
4. How long will 12 people survive on the vessel?
- Provisions last 6 days for 10 people.
- Calculate the total provisions available: [tex]\( 10 \times 6 = 60 \)[/tex] person-days.
- For 12 people, divide the total person-days by the number of people.
- [tex]\( \text{Days for 12 people} = \frac{60}{12} = 5 \)[/tex].
- So, 12 people will survive for 5 days.
5. If he wants to complete his journey in 4 hours, at what speed must he travel?
- Current travel time is 4.5 hours at 80 km/h.
- Calculate the total distance [tex]\( \text{Distance} = 80 \times 4.5 = 360 \)[/tex] km.
- He wants to cover this distance in 4 hours.
- Divide the distance by the time to find the speed.
- [tex]\( \text{Required speed} = \frac{360}{4} = 90 \)[/tex] km/h.
- So, he must travel at 90 km/h.
6. If he drives at 110 km/h, how long will the journey be? Give the answer in hours and minutes.
- Use the same distance: 360 km.
- Divide the distance by the new speed.
- [tex]\( \text{Time for journey} = \frac{360}{110} \approx 3.27 \)[/tex] hours.
- Convert 0.27 hours to minutes: [tex]\( 0.27 \times 60 \approx 16 \)[/tex] minutes.
- So, the journey will take 3 hours and 16 minutes.
I hope this clarifies the problem! Let me know if you have any more questions.
1. How many machines will you need to produce 500 items per hour?
- Each machine produces 100 items in one hour.
- To produce 500 items in one hour, you need several machines.
- Divide the target number of items (500) by the number of items one machine produces (100).
- [tex]\( \text{Number of machines needed} = \frac{500}{100} = 5 \)[/tex].
- So, you need 5 machines.
2. How long will it take 4 machines to produce 100 items?
- Each machine produces 100 items in one hour.
- Four machines combined produce [tex]\( 4 \times 100 = 400 \)[/tex] items in one hour.
- You need to produce 100 items.
- Divide the target number of items (100) by the total number of items produced by 4 machines in one hour (400).
- [tex]\( \text{Time required in hours} = \frac{100}{400} = 0.25 \)[/tex].
- So, it will take 0.25 hours, which is 15 minutes.
3. How many items do 8 machines produce in 45 minutes?
- Each machine produces 100 items in one hour.
- Eight machines produce [tex]\( 8 \times 100 = 800 \)[/tex] items in one hour.
- Convert 45 minutes to hours [tex]\( \text{(45 minutes)} = \frac{45}{60} \)[/tex] hours = 0.75 hours.
- Multiply the number of items produced by 8 machines in one hour by 0.75.
- [tex]\( \text{Items produced} = 800 \times 0.75 = 600 \)[/tex].
- So, 8 machines produce 600 items in 45 minutes.
4. How long will 12 people survive on the vessel?
- Provisions last 6 days for 10 people.
- Calculate the total provisions available: [tex]\( 10 \times 6 = 60 \)[/tex] person-days.
- For 12 people, divide the total person-days by the number of people.
- [tex]\( \text{Days for 12 people} = \frac{60}{12} = 5 \)[/tex].
- So, 12 people will survive for 5 days.
5. If he wants to complete his journey in 4 hours, at what speed must he travel?
- Current travel time is 4.5 hours at 80 km/h.
- Calculate the total distance [tex]\( \text{Distance} = 80 \times 4.5 = 360 \)[/tex] km.
- He wants to cover this distance in 4 hours.
- Divide the distance by the time to find the speed.
- [tex]\( \text{Required speed} = \frac{360}{4} = 90 \)[/tex] km/h.
- So, he must travel at 90 km/h.
6. If he drives at 110 km/h, how long will the journey be? Give the answer in hours and minutes.
- Use the same distance: 360 km.
- Divide the distance by the new speed.
- [tex]\( \text{Time for journey} = \frac{360}{110} \approx 3.27 \)[/tex] hours.
- Convert 0.27 hours to minutes: [tex]\( 0.27 \times 60 \approx 16 \)[/tex] minutes.
- So, the journey will take 3 hours and 16 minutes.
I hope this clarifies the problem! Let me know if you have any more questions.
