Final answer:
The speed of a car that makes the trip in 7 hours, when it is known that a trip taking 11 hours was done at 28 mph, can be found using inverse variation. The constant is the product of the speed and time, which is 308 for the first car. Using this constant, the speed for the second car is calculated to be 44 mph.
Step-by-step explanation:
The relationship between the time taken to travel between two cities and the speed of the car is an inverse variation. In this case, the product of the time taken and the speed is constant. When one of the values increases, the other decreases proportionally.
To find the speed of the car that makes the trip in 7 hours, we can use the information provided for the first car.
Let's denote the constant of variation by k. With the first car's speed (28 mph) and the time taken (11 hours), we can write the equation k = speed × time = 28 mph × 11 hours.
Solving this gives us k = 308.
Now for the second car which makes the trip in 7 hours, the speed (let's denote it as V) we are looking for can be found using the previously calculated constant k. We set up the equation V × 7 hours = 308.
Solving for V, we get V = 308 / 7 = 44 mph.
Therefore, the speed of a car that makes the trip in 7 hours is 44 mph.