The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes
5
hours for a car moving at
54 mph
. How long does the trip take for a car moving at
45 mph
?
5 * 54 = x * 45
To find out how long the trip takes for a car moving at 45 mph, we need to use the concept of inverse variation.
Inverse variation means that when one variable increases, the other variable decreases, and vice versa. In this case, the time it takes to cover the distance between two cities varies inversely with the speed of the car.
Let's set up a formula to represent this inverse variation:
time = k/speed
where k is the constant of variation.
We can plug in the values given in the problem to find the value of k. It says that the trip takes 5 hours for a car moving at 54 mph.
5 = k/54
To solve for k, we can multiply both sides of the equation by 54:
5 * 54 = k
k = 270
Now that we have the value of k, we can use it to find the time it takes for a car moving at 45 mph:
time = 270/45
time = 6 hours
Therefore, the trip takes 6 hours for a car moving at 45 mph.