Let \( c \) be the cost of one guitar pick. According to the problem, the cost of one guitar string would then be \( c + 1 \).
Patrick bought 25 guitar picks and 25 guitar strings, resulting in the total cost:
\[ 25c + 25(c + 1) = 40 \]
Simplifying this equation:
\[ 25c + 25c + 25 = 40 \] \[ 50c + 25 = 40 \]
Next, subtract 25 from both sides:
\[ 50c = 15 \]
Now, divide both sides by 50:
\[ c = \frac{15}{50} = \frac{3}{10} = 0.30 \]
Therefore, the cost of one guitar pick is $0.30. Now, we can find the cost of one guitar string:
\[ \text{Cost of one guitar string} = c + 1 = 0.30 + 1 = 1.30 \]
Thus, the cost of one guitar string is \( \boxed{1.30} \).
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