The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes
15 hours for a car moving at
54 mph. What is the speed of a car that makes the trip in 27
hours?
15 * 54 = s * 27
To solve this problem, we can use the concept of inverse variation.
Inverse variation, or inverse proportionality, means that as one variable increases, the other variable decreases, and vice versa. In other words, if one variable (in this case, the time) is multiplied by a constant, the other variable (in this case, the speed) is divided by the same constant, and the product remains constant.
Let's denote the time as "t" and the speed as "s". We are given that the trip takes 15 hours for a car moving at 54 mph, so we can write the inverse variation equation as:
t = k/s
where "k" is the constant of variation.
Substituting the given values, we have:
15 = k/54
To find the value of "k", we can cross-multiply and solve for it:
k = 15 * 54 = 810
Now, we can use this value of "k" to find the speed of a car that makes the trip in 27 hours:
27 = 810/s
To solve for "s", we can cross-multiply:
27s = 810
Finally, divide both sides by 27 to isolate "s":
s = 810/27
Simplifying the right side:
s = 30
Therefore, the speed of a car that makes the trip in 27 hours is 30 mph.