The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes
6
hours for a car moving at
30 mph
. How long does the trip take for a car moving at
18 mph
?
We can use the formula for inverse variation:
time = k/speed
where k is a constant of proportionality.
To find k, we can use the information given for the first scenario:
6 = k/30
Multiplying both sides by 30:
k = 180
Now we can use this value of k for the second scenario:
time = 180/18
time = 10
Therefore, the trip takes 10 hours for a car moving at 18 mph.
To solve this problem, we can use the concept of inverse variation. Inverse variation means that as one variable increases, the other variable decreases, and vice versa.
Let's denote the time it takes to cover the distance between the two cities as "t" and the speed of the car as "s".
According to the given information, when the car is moving at 30 mph, the trip takes 6 hours. So we can write this as an equation:
t = k/s
where k is the constant of variation.
We can use this equation to find the value of k:
6 = k/30
To find k, we can cross multiply:
6 * 30 = k
k = 180
Now that we have the value of k, we can use it to find the time it takes for a car moving at 18 mph:
t = 180/18
t = 10
Therefore, the trip takes 10 hours for a car moving at 18 mph.