Two pipes can fill a tank in 79 minutes if both are turned on. If only one is used, it would take 39 minutes longer for the smaller pipe to fill the tank than the larger pipe. How long will it take for the smaller pipe to fill the tank? (Round your answer to the nearest tenth.)

Step 1 ：Let's denote the time it takes for the larger pipe to fill the tank as \(L\) and the time it takes for the smaller pipe to fill the tank as \(S\).

Step 2 ：From the problem, we know that: \(\frac{1}{L} + \frac{1}{S} = \frac{1}{79}\) (since both pipes together can fill the tank in 79 minutes) and \(S = L + 39\) (since the smaller pipe takes 39 minutes longer than the larger pipe to fill the tank).

Step 3 ：We can substitute the second equation into the first to get: \(\frac{1}{L} + \frac{1}{L+39} = \frac{1}{79}\).

Step 4 ：To solve this equation, we first find a common denominator, which is \(L*(L+39)\), and rewrite the equation as: \((L+39) + L = \frac{L*(L+39)}{79}\).

Step 5 ：Simplify this to get: \(2L + 39 = \frac{L^2}{79} + \frac{39L}{79}\).

Step 6 ：Multiply every term by 79 to clear the fraction: \(158L + 3101 = L^2 + 39L\).

Step 7 ：Rearrange the equation to get a quadratic equation: \(L^2 - 119L + 3101 = 0\).

Step 8 ：We can solve this quadratic equation using the quadratic formula: \(L = \frac{119 ± \sqrt{(119)^2 - 4*1*3101}}{2*1}\).

Step 9 ：Simplify to get: \(L = \frac{119 ± \sqrt{14161 - 12404}}{2}\) and \(L = \frac{119 ± \sqrt{1757}}{2}\).

Step 10 ：We discard the negative solution because time cannot be negative, so: \(L = \frac{119 + 41.9}{2} = 80.45\) minutes.

Step 11 ：Substitute \(L = 80.45\) into the second equation: \(S = L + 39 = 80.45 + 39 = 119.45\) minutes.

Step 12 ：\(\boxed{S = 119.45}\) minutes. So, it will take approximately 119.5 minutes for the smaller pipe to fill the tank.