Two friends drive off in different directions from the same place. One heads North at 30 miles per hour, while the other heads East at 40 miles per hour. Complete an equation for the distance between the friends after t hours.

Step 1 ：Two friends drive off in different directions from the same place. One heads North at 30 miles per hour, while the other heads East at 40 miles per hour. We need to find an equation for the distance between the friends after t hours.

Step 2 ：The problem can be solved using the Pythagorean theorem. The distance between the two friends after t hours will be the hypotenuse of a right triangle, where the two sides are the distances each friend has traveled.

Step 3 ：The distance traveled by each friend is the speed times the time. So, the equation for the distance between the friends after t hours is \(\sqrt{(30t)^2 + (40t)^2}\).

Step 4 ：Using Python to simplify the equation, we get \(50t\).

Step 5 ：Final Answer: The equation for the distance between the friends after t hours is \(\boxed{50t}\).