Answer :
Certainly! Let's go through each question step-by-step.
### 1. How long will it take 4 machines to produce 100 items?
To find out how long it takes, we use the concept of rate. If we assume each machine produces 1 item per minute:
- Rate of 1 machine: 1 item per minute.
- Rate of 4 machines: 4 items per minute (since 4 machines each produce 1 item per minute).
We want to produce 100 items, so:
- Total time needed = Total items ÷ Rate of production = 100 items ÷ 4 items per minute = 25 minutes.
### 2. How many items do 8 machines produce in 45 minutes?
With 8 machines, each assumed to produce 1 item per minute:
- Rate of 8 machines: 8 items per minute.
In 45 minutes, the total production is:
- Items produced = Rate × Time = 8 items/minute × 45 minutes = 360 items.
### 3. If a rescue vessel has enough provisions for 10 people to survive for 6 days, how long will 12 people survive on the vessel?
This problem involves proportional reasoning:
- Total provisions measured in person-days = 10 people × 6 days = 60 person-days.
If there are 12 people on the vessel, the number of days they can survive is:
- Survival days = Total provisions ÷ Number of people = 60 person-days ÷ 12 people = 5 days.
### 4. A motorist takes 4.5 hours to reach his destination at 80 km/h. If he wants to complete his journey in 4 hours, at what speed must he travel?
Calculate the total distance first:
- Distance = Speed × Time = 80 km/h × 4.5 hours = 360 km.
If he wants to cover the same distance in 4 hours:
- Required speed = Distance ÷ Desired time = 360 km ÷ 4 hours = 90 km/h.
### 5. If he drives at 110 km/h, how long will the journey be?
Using the previously calculated distance of 360 km:
- Time = Distance ÷ Speed = 360 km ÷ 110 km/h ≈ 3.27 hours (approximately 3 hours and 16 minutes).
These are the detailed solutions for each question based on the information given.
### 1. How long will it take 4 machines to produce 100 items?
To find out how long it takes, we use the concept of rate. If we assume each machine produces 1 item per minute:
- Rate of 1 machine: 1 item per minute.
- Rate of 4 machines: 4 items per minute (since 4 machines each produce 1 item per minute).
We want to produce 100 items, so:
- Total time needed = Total items ÷ Rate of production = 100 items ÷ 4 items per minute = 25 minutes.
### 2. How many items do 8 machines produce in 45 minutes?
With 8 machines, each assumed to produce 1 item per minute:
- Rate of 8 machines: 8 items per minute.
In 45 minutes, the total production is:
- Items produced = Rate × Time = 8 items/minute × 45 minutes = 360 items.
### 3. If a rescue vessel has enough provisions for 10 people to survive for 6 days, how long will 12 people survive on the vessel?
This problem involves proportional reasoning:
- Total provisions measured in person-days = 10 people × 6 days = 60 person-days.
If there are 12 people on the vessel, the number of days they can survive is:
- Survival days = Total provisions ÷ Number of people = 60 person-days ÷ 12 people = 5 days.
### 4. A motorist takes 4.5 hours to reach his destination at 80 km/h. If he wants to complete his journey in 4 hours, at what speed must he travel?
Calculate the total distance first:
- Distance = Speed × Time = 80 km/h × 4.5 hours = 360 km.
If he wants to cover the same distance in 4 hours:
- Required speed = Distance ÷ Desired time = 360 km ÷ 4 hours = 90 km/h.
### 5. If he drives at 110 km/h, how long will the journey be?
Using the previously calculated distance of 360 km:
- Time = Distance ÷ Speed = 360 km ÷ 110 km/h ≈ 3.27 hours (approximately 3 hours and 16 minutes).
These are the detailed solutions for each question based on the information given.
