the time it takes to cover the distance between two cities by car varies inversely with the speed of the car. the trip takes 10 hours for a car moving at 39 mph. how long does the trip take for a car moving at 26 mph?
The distance between the cities:
10 ∙ 39 = 390 mi
When two variables are inversely proportional, their product is equal to a constant.
In this case distance = time ∙ speed
d = t ∙ v
390 = t ∙ 26
t = 390 / 26 = 15 h
To solve this problem, we need to use the inverse variation formula.
Let's represent 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 problem, we know that the trip takes 10 hours for a car moving at 39 mph.
Inverse variation equation: t = k/s
Where "k" represents the constant of variation.
To find the constant of variation, plug in the values we have:
10 = k/39 (since the trip takes 10 hours for a car moving at 39 mph)
Now, to find the time it takes for the car moving at 26 mph, we'll use the same equation and solve for "t":
t = k/26
Let's substitute the value of "k" that we found earlier and solve for "t":
10 = k/39
k = 10 * 39
k = 390
Now, substitute the value of "k" into the equation for the car moving at 26 mph:
t = 390/26
t = 15
Therefore, the trip takes 15 hours for a car moving at 26 mph.