A car drives east along a road at a constant speed of 46 miles per hour. At 4:00 P.M., a truck is 264 miles away, driving west along the same road at a constant speed. The vehicles pass each other at 7:00 P.M. What is the speed of the truck?
To find the speed of the truck, we can start by determining the time it takes for the vehicles to pass each other. We know that the car drives east at a constant speed of 46 miles per hour, so in 3 hours (from 4:00 P.M. to 7:00 P.M.), it would have traveled a distance of 46 miles/hour × 3 hours = 138 miles.
Since the total distance between the car and the truck is 264 miles, and the car has already traveled 138 miles, the remaining distance that the truck needs to travel is 264 miles - 138 miles = 126 miles.
Now, we can find the speed of the truck by dividing the remaining distance by the time it took for the vehicles to pass each other. So the speed of the truck is 126 miles ÷ 3 hours = 42 miles per hour.
Therefore, the speed of the truck is 42 miles per hour.
To find the speed of the truck, we need to determine the time it took for the vehicles to pass each other. Once we know the time, we can calculate the speed using the formula: Speed = Distance / Time.
In this problem, the car and truck are traveling in opposite directions, so we can add their speeds together to determine the relative speed at which they are approaching each other.
Given:
Car's speed = 46 miles per hour
Car and truck passed each other at 7:00 P.M.
Starting at 4:00 P.M. (3 hours earlier), the truck was 264 miles away.
To find the time it took for the vehicles to pass each other, we subtract the starting distance of the truck from the total distance traveled by both vehicles:
Total Distance = Distance covered by the car + Distance covered by the truck = 264 miles + 264 miles = 528 miles.
Now, let's calculate the time it took for the vehicles to pass each other:
Total Time = Time taken by the car + Time taken by the truck = t + 3 hours.
Since we have the distance and relative speed, we can use the formula: Distance = Speed * Time to calculate the time taken by each vehicle:
Distance covered by the car = Car's speed * Time taken by the car = 46 * (t + 3).
Distance covered by the truck = Truck's speed * Time taken by the truck.
Since the total distance covered by both vehicles is 528 miles, we can write the equation:
264 = 46 * (t + 3) + Truck's speed * Time taken by the truck.
From this equation, we can see that we need one more equation to solve for two unknown variables, which are the Truck's speed and Time taken by the truck.
Unfortunately, the problem statement does not provide additional information, such as the relationship between the car and truck speeds. Without this information, it is not possible to determine the speed of the truck.
speed = distance/time, so, since 3 hours passed,
46+x = 264/3