Let \( c \) be the cost of one guitar pick. Since the cost of one guitar string is \( c + 1 \), we can set up the equation based on the total cost for purchasing 25 guitar picks and 25 guitar strings.
The total cost can be expressed as:
\[ 25c + 25(c + 1) = 40 \]
Now, let's simplify the equation:
\[ 25c + 25c + 25 = 40 \]
Combining like terms:
\[ 50c + 25 = 40 \]
Next, subtract 25 from both sides:
\[ 50c = 15 \]
Now, divide both sides by 50:
\[ c = \frac{15}{50} = \frac{3}{10} = 0.30 \]
Now that we have the cost of one guitar pick, we can find the cost of one guitar string:
\[ c + 1 = 0.30 + 1 = 1.30 \]
Thus, the cost of one guitar string is \(\boxed{1.30}\).