Answer :
Certainly! Let's break down the problem into a step-by-step solution to understand how much fuel the machine will use in 7 hours and 30 minutes.
### Step 1: Understand the Given Information
1. Fuel Consumption: The machine uses [tex]\(3 \frac{3}{4}\)[/tex] litres of fuel every 4 hours.
- Convert [tex]\(3 \frac{3}{4}\)[/tex] to a decimal: [tex]\(3 + \frac{3}{4} = 3.75\)[/tex] litres.
2. Time Period: We need to find the fuel consumption for a time period of 7 hours and 30 minutes.
- Convert 30 minutes to hours: [tex]\[ 30 \text{ minutes} = \frac{30}{60} \text{ hours} = 0.5 \text{ hours} \][/tex]
- So, the total time is [tex]\(7 \text{ hours} + 0.5 \text{ hours} = 7.5 \text{ hours}\)[/tex].
### Step 2: Find the Fuel Consumption Rate per Hour
To determine the fuel consumption rate per hour, we divide the total fuel used in 4 hours by 4:
[tex]\[ \text{Fuel per hour} = \frac{3.75 \text{ litres}}{4 \text{ hours}} = 0.9375 \text{ litres per hour} \][/tex]
### Step 3: Calculate the Total Fuel Used in 7.5 Hours
Now that we have the rate of fuel consumption per hour, we can find the total fuel consumption over 7.5 hours by multiplying the hourly rate by the total time:
[tex]\[ \text{Total fuel used} = 0.9375 \text{ litres per hour} \times 7.5 \text{ hours} = 7.03125 \text{ litres} \][/tex]
### Summary
The machine uses approximately 0.9375 litres of fuel per hour. Over a period of 7 hours and 30 minutes, the total fuel consumption will be about 7.03125 litres.
Therefore, the machine will use 7.03125 litres of petrol in 7 hours and 30 minutes.
### Step 1: Understand the Given Information
1. Fuel Consumption: The machine uses [tex]\(3 \frac{3}{4}\)[/tex] litres of fuel every 4 hours.
- Convert [tex]\(3 \frac{3}{4}\)[/tex] to a decimal: [tex]\(3 + \frac{3}{4} = 3.75\)[/tex] litres.
2. Time Period: We need to find the fuel consumption for a time period of 7 hours and 30 minutes.
- Convert 30 minutes to hours: [tex]\[ 30 \text{ minutes} = \frac{30}{60} \text{ hours} = 0.5 \text{ hours} \][/tex]
- So, the total time is [tex]\(7 \text{ hours} + 0.5 \text{ hours} = 7.5 \text{ hours}\)[/tex].
### Step 2: Find the Fuel Consumption Rate per Hour
To determine the fuel consumption rate per hour, we divide the total fuel used in 4 hours by 4:
[tex]\[ \text{Fuel per hour} = \frac{3.75 \text{ litres}}{4 \text{ hours}} = 0.9375 \text{ litres per hour} \][/tex]
### Step 3: Calculate the Total Fuel Used in 7.5 Hours
Now that we have the rate of fuel consumption per hour, we can find the total fuel consumption over 7.5 hours by multiplying the hourly rate by the total time:
[tex]\[ \text{Total fuel used} = 0.9375 \text{ litres per hour} \times 7.5 \text{ hours} = 7.03125 \text{ litres} \][/tex]
### Summary
The machine uses approximately 0.9375 litres of fuel per hour. Over a period of 7 hours and 30 minutes, the total fuel consumption will be about 7.03125 litres.
Therefore, the machine will use 7.03125 litres of petrol in 7 hours and 30 minutes.
