Calculate concentration gradients in FPLC

Our FPLC works with two solutions:



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> A: 20 mM Tris.HCl, 0.2 M NaCl, pH 7.8
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> B: 20 mM Tris.HCl, 1.6 M NaCl, pH 7.8
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I'm interested in sample volume from 102 mL to 117 mL. The FPLC will have a linear concentration gradient: At 24 mL it will be 75% A and at 144 mL it will be 5% A (the rest is filled up with B).


For visualization, I made a graph (y = -7/1200\*x + 0.89):
[![enter image description here](https://i.stack.imgur.com/K0Bzd.png)](https://i.stack.imgur.com/K0Bzd.png)


Now, I have a sample with the *whole output between the two indicated points* (102 mL and 117 mL, so I have 15 mL in my tube) and would like to calculate the NaCl concentration.




Percentage of both A and B would change 70% from 24 to 144mL, with A from 75% to 5% and B from 25% up to 95%. The change rate would be 70% during the 120mL period or $0.70/120$ per mL. At any given point $x$ mL, between 24 and 144mL, concentration of $\ce{NaCl}$ in $\ce{mol/L}$ is: $$\ce{[NaCl]} = (0.75 - 0.7\times (x-24)/120)\times0.2 + (0.25 + 0.7\times (x-24)/120)\times1.6$$ 


For a 15mL solution between 102 and 117mL, the concentration should be the average of the two points when x = 102, and 117mL.


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In addition to Dejian15's answer, which is probably the simplest, I also figured out a solution for a general curve (also non-linear ones).
$$ \frac{\int^{117}\_{102}(\frac{-7}{1200}x+0.89)\*0.2+(1-(\frac{-7}{1200}x+0.89))\*1.6~\mathrm{ d}x }{15} =1.24826$$


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