Question

Until the truck runs out of gas, the amount of gas in its fuel tank varies inversely with the number of miles traveled. With 9 gallons left, the truck has traveled 135 miles. How many gallons are left once the truck has traveled 225 miles?

Answer 1

After traveling 225 miles, there would be 5.4 gallons of gasoline left in the truck's fuel tank based on the inverse variation relationship between the miles traveled and the gallons remaining.

Step-by-step explanation:

The question concerns an inverse variation problem in long-haul trucking. This type of variation means that as one quantity increases, another quantity decreases in such a way that their product is constant. Given that the truck has traveled 135 miles with 9 gallons left, we can calculate the constant of variation. The constant (k) is obtained by multiplying the number of gallons by the number of miles (k = miles * gallons).

First, calculate the constant using the information provided:

• k = 9 gallons * 135 miles = 1215 gallon-miles.

Now, we need to find out how many gallons are left after the truck has traveled 225 miles. We use the constant of variation:

• gallons = k / miles
• gallons = 1215 gallon-miles / 225 miles
• gallons = 5.4 gallons left after the truck has traveled 225 miles.

Thus, there will be 5.4 gallons of gasoline left once the truck has traveled 225 miles, assuming the inverse variation relationship continues.