Sure, let's go through the problem step-by-step in detail.
We start with the given information:
1. A car travels 108 kilometers using 3 gallons of fuel in 2 hours.
We need to find out:
1. The distance the car can travel using 5 gallons of fuel.
2. The distance the car can travel in 3.5 hours.
### Step 1: Calculate the distance per gallon.
First, we determine how far the car travels using 1 gallon of fuel.
[tex]\[
\text{Distance per gallon} = \frac{\text{Total distance}}{\text{Total gallons}} = \frac{108 \, \text{km}}{3 \, \text{gallons}} = 36 \, \text{km/gallon}
\][/tex]
### Step 2: Calculate the speed in kilometers per hour (km/h).
Next, we determine the car's speed.
[tex]\[
\text{Speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{108 \, \text{km}}{2 \, \text{hours}} = 54 \, \text{km/h}
\][/tex]
### Step 3: Calculate the distance with 5 gallons of fuel.
Using the distance per gallon, we can find the distance the car can travel with 5 gallons.
[tex]\[
\text{Distance with 5 gallons} = \text{Distance per gallon} \times 5 = 36 \, \text{km/gallon} \times 5 = 180 \, \text{km}
\][/tex]
### Step 4: Calculate the distance in 3.5 hours.
Using the speed of the car, we can determine the distance it can travel in 3.5 hours.
[tex]\[
\text{Distance in 3.5 hours} = \text{Speed} \times \text{Time} = 54 \, \text{km/h} \times 3.5 \, \text{hours} = 189 \, \text{km}
\][/tex]
### Summary
From the calculations:
- The distance traveled per gallon of fuel is 36 km.
- The speed of the car is 54 km/h.
- The distance the car can travel with 5 gallons of fuel is 180 km.
- The distance the car can travel in 3.5 hours is 189 km.
These values match the provided answer:
[tex]\[
(36.0, 54.0, 180.0, 189.0)
\][/tex]
