Final answer:
By using the joint variation equation, after finding the constant of variation from the given trip, it was determined that approximately 38.4 liters of gasoline will be used on a 192 kilometer trip at 64 km/hr.
Step-by-step explanation:
The amount of gasoline used by a car varies jointly with the distance traveled and the square root of the speed. Given that a car used 25 liters on a 100 kilometer trip at 100 km/hr, we can set up the joint variation equation as follows:
Gasoline (G) = k × Distance (D) × sqrt(Speed (S))
For the given trip:
25 = k × 100 × sqrt(100)
25 = k × 100 × 10
k = 25 / 1000
k = 0.025
We can then use this value of k to calculate the gasoline used on a 192 kilometer trip at 64 km/hr:
G = 0.025 × 192 × sqrt(64)
G = 0.025 × 192 × 8
G = 0.025 × 1536
G = 38.4 liters
Therefore, the car will use approximately 38.4 liters of gasoline on the 192 kilometer trip at 64 km/hr.