Let the cost of one guitar pick be \( c \). Since the guitar strings cost $1 more than the guitar picks, the cost of one guitar string will be \( c + 1 \).
Patrick bought 25 guitar picks and 25 guitar strings, so the total cost can be expressed as:
\[ 25c + 25(c + 1) \]
This simplifies to:
\[ 25c + 25c + 25 = 50c + 25 \]
According to the problem, the total amount spent is $40, so we can set up the equation:
\[ 50c + 25 = 40 \]
To solve for \( c \), first, subtract 25 from both sides:
\[ 50c = 15 \]
Next, divide 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:
\[ \boxed{1.30} \]
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