Final answer:
To find the van's average speed, we can use the formula: average speed = total distance / total time. Given that the truck traveled for 3 hours at 85 mph and the vehicles were 488 miles apart, the van's average speed is approximately 77.67 mph.
Step-by-step explanation:
To find the van's average speed, we can use the formula:
average speed = total distance / total time
We know that the truck traveled for 3 hours at a speed of 85 mph, and the vehicles were 488 miles apart. Using this information, we can calculate the total time taken by the van to travel:
total time = truck's time + van's time
Given that the van and truck traveled in opposite directions, the van and truck combined covered a distance of 488 miles:
distance covered by truck + distance covered by van = 488 miles
Since the truck traveled for 3 hours at 85 mph, the distance covered by the truck is:
distance covered by truck = truck's speed × truck's time = 85 mph × 3 hours
Substituting the known values into the equation for the distance covered by the truck:
85 mph × 3 hours + distance covered by van = 488 miles
Simplifying the equation:
255 miles + distance covered by van = 488 miles
distance covered by van = 488 miles - 255 miles
distance covered by van = 233 miles
Now that we know the distance covered by the van is 233 miles and the time taken by the van and truck combined is 3 hours, we can use the average speed formula to find the van's average speed:
average speed = total distance / total time = 233 miles / 3 hours
Calculating the average speed:
average speed ≈ 77.67 mph
Therefore, the van's average speed is approximately 77.67 mph.