To solve the problem, let's define the speeds of Ned and Ralph.
Let:
- \( r \) be Ralph's speed in miles per hour.
- \( r + 5 \) be Ned's speed (since he drives 5 mph faster than Ralph).
Both of them left the auditorium at the same time and after 2 hours they were 250 miles apart. The total distance they covered is the sum of the distances each of them drove.
The distance covered by Ralph in 2 hours is: \[ \text{Distance}_{Ralph} = r \times 2 \]
The distance covered by Ned in 2 hours is: \[ \text{Distance}_{Ned} = (r + 5) \times 2 \]
Adding these two distances gives the total distance they are apart: \[ 2r + 2(r + 5) = 250 \]
Now, let's simplify this equation: \[ 2r + 2r + 10 = 250 \] \[ 4r + 10 = 250 \]
Next, we subtract 10 from both sides: \[ 4r = 240 \]
Now we divide both sides by 4: \[ r = 60 \]
Thus, Ralph's speed is \( 60 \) miles per hour.
To check:
- Ralph's distance in 2 hours: \( 60 \times 2 = 120 \) miles.
- Ned's speed: \( 60 + 5 = 65 \) miles per hour.
- Ned's distance in 2 hours: \( 65 \times 2 = 130 \) miles.
- Total distance apart: \( 120 + 130 = 250 \) miles.
The calculations confirm the solution is consistent. Therefore, Ralph drove at a speed of: \[ \boxed{60} \text{ miles per hour.} \]