Answer :
To determine how much petrol Tony uses for his trip with the given conditions, we need to analyze the journey in two segments and calculate the fuel consumption for each, based on the provided mileage rates.
### Step 1: Analyzing the First Segment
Tony drives the first 13 miles in 13 minutes. First, we convert time into hours:
[tex]\[ \text{Time} = \frac{13 \text{ minutes}}{60} \approx 0.21667 \text{ hours} \][/tex]
During this segment, Tony's speed is:
[tex]\[ \text{Speed} = \frac{13 \text{ miles}}{0.21667 \text{ hours}} \approx 60 \text{ mph} \][/tex]
Since his speed is 65 mph or less, he uses fuel at the rate of 50 miles per gallon (mpg).
Fuel consumed in the first segment:
[tex]\[ \text{Fuel}_{\text{initial}} = \frac{13 \text{ miles}}{50 \text{ mpg}} = 0.26 \text{ gallons} \][/tex]
### Step 2: Analyzing the Second Segment
Tony continues his journey at an average speed of 68 mph for 1 hour and 24 minutes. We must convert 1 hour 24 minutes to hours:
[tex]\[ 1 \text{ hour} + \frac{24 \text{ minutes}}{60} = 1 + 0.4 = 1.4 \text{ hours} \][/tex]
During this segment, the distance covered is:
[tex]\[ \text{Distance} = 68 \text{ mph} \times 1.4 \text{ hours} = 95.2 \text{ miles} \][/tex]
Since his speed is greater than 65 mph, he uses fuel at the rate of 40 mpg.
Fuel consumed in the second segment:
[tex]\[ \text{Fuel}_{\text{remaining}} = \frac{95.2 \text{ miles}}{40 \text{ mpg}} = 2.38 \text{ gallons} \][/tex]
### Step 3: Calculating Total Fuel Consumed
Finally, the total fuel consumed for both segments is the sum of the fuel used in each segment:
[tex]\[ \text{Total Fuel} = \text{Fuel}_{\text{initial}} + \text{Fuel}_{\text{remaining}} = 0.26 \text{ gallons} + 2.38 \text{ gallons} = 2.64 \text{ gallons} \][/tex]
Thus, Tony uses a total of 2.64 gallons of petrol for his trip.
### Step 1: Analyzing the First Segment
Tony drives the first 13 miles in 13 minutes. First, we convert time into hours:
[tex]\[ \text{Time} = \frac{13 \text{ minutes}}{60} \approx 0.21667 \text{ hours} \][/tex]
During this segment, Tony's speed is:
[tex]\[ \text{Speed} = \frac{13 \text{ miles}}{0.21667 \text{ hours}} \approx 60 \text{ mph} \][/tex]
Since his speed is 65 mph or less, he uses fuel at the rate of 50 miles per gallon (mpg).
Fuel consumed in the first segment:
[tex]\[ \text{Fuel}_{\text{initial}} = \frac{13 \text{ miles}}{50 \text{ mpg}} = 0.26 \text{ gallons} \][/tex]
### Step 2: Analyzing the Second Segment
Tony continues his journey at an average speed of 68 mph for 1 hour and 24 minutes. We must convert 1 hour 24 minutes to hours:
[tex]\[ 1 \text{ hour} + \frac{24 \text{ minutes}}{60} = 1 + 0.4 = 1.4 \text{ hours} \][/tex]
During this segment, the distance covered is:
[tex]\[ \text{Distance} = 68 \text{ mph} \times 1.4 \text{ hours} = 95.2 \text{ miles} \][/tex]
Since his speed is greater than 65 mph, he uses fuel at the rate of 40 mpg.
Fuel consumed in the second segment:
[tex]\[ \text{Fuel}_{\text{remaining}} = \frac{95.2 \text{ miles}}{40 \text{ mpg}} = 2.38 \text{ gallons} \][/tex]
### Step 3: Calculating Total Fuel Consumed
Finally, the total fuel consumed for both segments is the sum of the fuel used in each segment:
[tex]\[ \text{Total Fuel} = \text{Fuel}_{\text{initial}} + \text{Fuel}_{\text{remaining}} = 0.26 \text{ gallons} + 2.38 \text{ gallons} = 2.64 \text{ gallons} \][/tex]
Thus, Tony uses a total of 2.64 gallons of petrol for his trip.
