Two cars leave the same point at noon. One car travels North and the other car travels East. Suppose the North bound car is travling 40mph and after two hours, the two cars are 100 miles apart. How fast is the other car going?
Your diagram should be a right-angled triangle with sides 80, 2r, and hypotenuse 100
(2r)^2 + 80^2 = 100^2
4r^2 = 3600
r^2 = 900
r = √900 = 30
The other car was going 30 mph
To find the speed of the Eastbound car, we need to determine the distance it has traveled in the same time frame as the Northbound car.
The Northbound car travels at a constant speed of 40 mph for 2 hours, so its distance traveled is:
Distance = Speed × Time = 40 mph × 2 hours = 80 miles.
Since the two cars are 100 miles apart after 2 hours, and the Northbound car has traveled 80 miles, the remaining distance is covered by the Eastbound car.
Distance traveled by the Eastbound car = Total distance - Distance traveled by the Northbound car
= 100 miles - 80 miles = 20 miles.
Now, we can calculate the Eastbound car's speed:
Speed = Distance / Time = 20 miles ÷ 2 hours = 10 mph.
Therefore, the speed of the Eastbound car is 10 mph.