The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes 8 hours for a car moving at 39 mph . How long does the trip take for a car moving at 52 mph ?
Let's denote the time it takes to cover the distance as \( t \), the speed of the car as \( s \), and the distance between the two cities as \( d \).
We can write the relationship as:
\( t = k \times \frac{d}{s} \)
Where \( k \) is a constant.
When the car is moving at 39 mph and the trip takes 8 hours:
\( 8 = k \times \frac{d}{39} \)
When the car is moving at 52 mph, we can set up another equation:
\( t = k \times \frac{d}{52} \)
Now, we can solve for \( t \) when the car is moving at 52 mph:
\( t = 8 \times \frac{39}{52} \)
\( t = 8 \times \frac{3}{4} \)
\( t = 6 \)
Therefore, the trip takes 6 hours for a car moving at 52 mph.