Final answer:
The time taken to complete the same trip at a speed of 85 mph would be approximately 39 minutes, based on the inverse variation relationship between time and speed.
Step-by-step explanation:
On a car trip, the time of trip varies inversely with the speed traveled. If one car drove at 51 mph and it took 65 minutes, we can use this information to determine how long it would take a different car to make the same trip at a speed of 85 mph.
Firstly, we need to establish a relation between speed and time for the given situation. The product of the speed and time is a constant in inverse variation. For the first car, the constant (k) can be calculated as:
Time × Speed = Constant
65 min × 51 mph = 3315 min·mph
To find the time it would take at 85 mph, we divide the constant by the new speed:
Constant / New Speed = New Time
3315 min·mph / 85 mph = 39 minutes
So, if the different car made the same trip at a speed of 85 mph, it would take approximately 39 minutes.