Answer :
Sure! Let's solve each part of the question step-by-step:
### 3.11: How many machines will you need to produce 500 items per hour?
- A single machine produces 100 items in one hour.
- To produce 500 items, you'll need more machines working together.
- The number of machines required is 500 divided by 100.
- Therefore, you need 5 machines.
### 3.12: How long will it take 4 machines to produce 100 items?
- One machine produces 100 items in one hour.
- With 4 machines, the productivity is multiplied by 4.
- Therefore, 4 machines can produce 100 items much faster.
- Time taken is 100 divided by (4 times 100).
- It will take 0.25 hours or 15 minutes.
### 313: How many items do 8 machines produce in 45 minutes?
- In one hour, one machine produces 100 items.
- So, in 45 minutes (which is 0.75 hours), a single machine will produce 100 times 0.75 items.
- Multiply the result by 8 as there are 8 machines.
- Therefore, 8 machines will produce 600 items in 45 minutes.
### 3.2: How long will 12 people survive on the vessel?
- The provisions are enough for 10 people to survive for 6 days.
- Thus, the total provisions are equivalent to 10 times 6 person-days.
- If 12 people are sharing these provisions, we need to divide the total person-days by 12.
- These provisions will last 5 days for 12 people.
### 331: If he wants to complete his journey in 4 hours, at what speed must he travel?
- The motorist originally takes 4.5 hours at a speed of 80 km/h.
- The distance can be found by multiplying speed by time: 80 km/h times 4.5 hours.
- To complete the same distance in 4 hours, divide the distance by 4 hours to find the required speed.
- Therefore, the motorist must travel at a speed of 90 km/h.
### 332: If he drives at 110 km/h, how long will the journey be? Give the answer in hours and minutes.
- Using the same original distance (calculated using 80 km/h and 4.5 hours), divide by new speed, which is 110 km/h.
- Convert the total time in hours to hours and minutes.
- The journey will take 3 hours and 16 minutes.
These steps show how you can break down each part of the question to arrive at the solution. If you have any more questions or need further clarification, feel free to ask!
### 3.11: How many machines will you need to produce 500 items per hour?
- A single machine produces 100 items in one hour.
- To produce 500 items, you'll need more machines working together.
- The number of machines required is 500 divided by 100.
- Therefore, you need 5 machines.
### 3.12: How long will it take 4 machines to produce 100 items?
- One machine produces 100 items in one hour.
- With 4 machines, the productivity is multiplied by 4.
- Therefore, 4 machines can produce 100 items much faster.
- Time taken is 100 divided by (4 times 100).
- It will take 0.25 hours or 15 minutes.
### 313: How many items do 8 machines produce in 45 minutes?
- In one hour, one machine produces 100 items.
- So, in 45 minutes (which is 0.75 hours), a single machine will produce 100 times 0.75 items.
- Multiply the result by 8 as there are 8 machines.
- Therefore, 8 machines will produce 600 items in 45 minutes.
### 3.2: How long will 12 people survive on the vessel?
- The provisions are enough for 10 people to survive for 6 days.
- Thus, the total provisions are equivalent to 10 times 6 person-days.
- If 12 people are sharing these provisions, we need to divide the total person-days by 12.
- These provisions will last 5 days for 12 people.
### 331: If he wants to complete his journey in 4 hours, at what speed must he travel?
- The motorist originally takes 4.5 hours at a speed of 80 km/h.
- The distance can be found by multiplying speed by time: 80 km/h times 4.5 hours.
- To complete the same distance in 4 hours, divide the distance by 4 hours to find the required speed.
- Therefore, the motorist must travel at a speed of 90 km/h.
### 332: If he drives at 110 km/h, how long will the journey be? Give the answer in hours and minutes.
- Using the same original distance (calculated using 80 km/h and 4.5 hours), divide by new speed, which is 110 km/h.
- Convert the total time in hours to hours and minutes.
- The journey will take 3 hours and 16 minutes.
These steps show how you can break down each part of the question to arrive at the solution. If you have any more questions or need further clarification, feel free to ask!
