A certain generator will run for 1.5 miles on one liter of gas. If the gas tank has the shape of a rectangular box that is 25 cm by 20 cm by 16 cm, how long will the generator run on a full tank of gas? [ 1 liter= 1,000 cubic centimeters]

Answer

To solve the problem step by step, we will calculate the volume of the gas tank, convert that volume into liters, and then determine how far the generator can run on that amount of gas.

### Step 1: Calculate the volume of the gas tank
The gas tank is in the shape of a rectangular box, and its volume \( V \) can be calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Given dimensions are:
- Length = 25 cm
- Width = 20 cm
- Height = 16 cm

Now, substituting the values:
\[ V = 25 \, \text{cm} \times 20 \, \text{cm} \times 16 \, \text{cm} \]

Calculating this step by step:
1. \( 25 \times 20 = 500 \)
2. \( 500 \times 16 = 8000 \)

Thus, the volume of the gas tank is:
\[ V = 8000 \, \text{cm}^3 \]

### Step 2: Convert cubic centimeters to liters
We know that:
\[ 1 \, \text{liter} = 1000 \, \text{cm}^3 \]
To find out how many liters are in 8000 cm³, we divide by 1000:
\[ \text{Liters} = \frac{8000 \, \text{cm}^3}{1000 \, \text{cm}^3/\text{liter}} = 8 \, \text{liters} \]

### Step 3: Calculate the distance the generator can run
The generator runs for 1.5 miles on 1 liter of gas. Therefore, for 8 liters, we can use the unitary method:
\[ \text{Distance} = 1.5 \, \text{miles/liter} \times 8 \, \text{liters} \]
Calculating this:
\[ \text{Distance} = 1.5 \times 8 = 12 \, \text{miles} \]

### Conclusion
The generator will run for a total distance of:
\[ \text{Distance} = 12 \, \text{miles} \]

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