two cars leave the same point at noon. one car travels north and the other car travels east. suppose the northbound car is traveling 40mph, and after two hours, the two car are 100 miles apart.how fast is the other car going?
recall that speed is distance travelled over time.
let x = speed of the other car.
then we set-up the equation.
when you draw the directions they're travelling, you will form a right triangle. thus recall that in a right triangle, the hypotenuse (in this the the distance between them which is 100 miles) is given by the Pythagorean theorem:
c^2 = a^2 + b^2
we equate distances:
100^2 = (40*2)^2 + (2x)^2
10000 = 80^2 + 4x^2
10000 - 6400 = 4x^2
3600 = 4x^2
x^2 = 900
x = 30 mph
hope this helps~ :)
To find the speed of the eastbound car, we can use the concept of distance, speed, and time. Here's how you can calculate it step by step:
1. First, we'll determine the total distance traveled by the northbound car after two hours. Since the northbound car is traveling at a constant speed of 40 mph and it has been traveling for 2 hours, the distance it has traveled is:
Distance = Speed × Time = 40 mph × 2 hours = 80 miles
2. Next, we'll use the Pythagorean theorem to calculate the distance between the two cars after two hours. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the northbound car's distance is one side, and the eastbound car's distance is the other side, while the distance between them is the hypotenuse.
So, using the Pythagorean theorem:
Hypotenuse² = Northbound Distance² + Eastbound Distance²
100 miles² = 80 miles² + Eastbound Distance²
3. Now, let's solve for the eastbound distance:
Eastbound Distance² = 100 miles² - 80 miles²
Eastbound Distance² = 10,000 miles² - 6,400 miles²
Eastbound Distance² = 3,600 miles²
4. To find the eastbound distance, we'll take the square root of both sides:
Eastbound Distance = √(3,600 miles²)
Eastbound Distance = 60 miles
5. Finally, to find the speed of the eastbound car, we'll divide the eastbound distance by the time it took to travel that distance. Since we know the eastbound car traveled for 2 hours as well, we can calculate its speed as:
Speed = Eastbound Distance ÷ Time = 60 miles ÷ 2 hours = 30 mph
Therefore, the eastbound car is traveling at a speed of 30 mph.