A car and a truck left Washington, DC traveling in opposite directions. The car traveled 19 miles per hour faster than the truck, and at the end of 8 hours they were 1448 miles apart. What was the average speed of each vehicle?
To find the average speed of each vehicle, we'll first need to determine the distance traveled by each vehicle. Let's start by understanding the information given:
1. The car traveled 19 miles per hour faster than the truck.
2. At the end of 8 hours, they were 1448 miles apart.
Let's assume the speed of the truck is represented by 'x' miles per hour. According to the information given, the speed of the car would be 'x + 19' miles per hour.
To calculate the distance traveled by the truck, we'll use the formula:
Distance = Speed × Time
For the truck: Distance_truck = x miles/hour × 8 hours
For the car: Distance_car = (x + 19) miles/hour × 8 hours
Now, let's calculate the distances traveled:
Distance_truck = 8x miles
Distance_car = 8(x + 19) miles
Given that the total distance between the car and truck is 1448 miles, we can set up the following equation:
Distance_truck + Distance_car = 1448
Substituting the values, we get:
8x + 8(x + 19) = 1448
Simplifying the equation:
8x + 8x + 152 = 1448
16x = 1296
x = 81
So, the speed of the truck is 81 miles per hour. To find the speed of the car, we can substitute the value of x back into the equation:
Speed_car = x + 19 = 81 + 19 = 100 miles per hour
Therefore, the average speed of the truck is 81 miles per hour, and the average speed of the car is 100 miles per hour.
let the velocity of the truck be V.
relative distance=relativevelocity*time
1448=(2v+19)/8
solve for v, the velocity of the truck. Then v+19 is the velocity of the car.