Two automobiles leave an intersection at the same time. One of them travels west and the other travels south. When the vehicle going south has traveled 24 miles, the distance between the cars was four miles more than 3 times the distance traveled by the vehicle traveling west. Find the distance between the two automobiles at that time.
If the westbound car has gone a distance w, then
w^2 + 24^2 = (3w+4)^2
To find the distance between the two automobiles at that time, we need to set up a system of equations based on the information given.
Let's assume that the distance traveled by the vehicle traveling west is represented by "x" miles.
According to the problem, when the vehicle going south has traveled 24 miles, the distance between the cars was four miles more than 3 times the distance traveled by the vehicle traveling west.
So, the distance between the two cars can be represented as 3x + 4 miles.
Now, let's set up the system of equations:
Equation 1: Distance traveled by the vehicle going south = 24 miles
Equation 2: Distance between the two cars = 3x + 4 miles
Since both automobiles left the intersection at the same time, we can equate the distances traveled by each vehicle.
x = 24
Now we can substitute this value into Equation 2:
Distance between the two cars = 3(24) + 4
Distance between the two cars = 72 + 4
Distance between the two cars = 76 miles
Therefore, the distance between the two automobiles at that time is 76 miles.