1. The problem statement, all variables and given/known data

See attachement titled p8.jpg

2. Relevant equations
The following equations apply to a cantilevered beam held fixed on the left end:

$$\delta_{max} = -\frac{PL^3}{3EI}$$

$$\theta = -\frac{PL^2}{2EI}$$

$$\delta = \frac{P}{6EI}(x^3-3Lx^2)$$

The following equations apply to a simply supported beam with a constant distrubuted load:

$$\delta_{max} = -\frac{5\omega L^4}{384EI}$$

$$\theta = -\frac{\omega L^3}{24EI}$$

$$\delta = -\frac{\omega}{24EI}(x^4-2Lx^3+L^3x)$$

3. The attempt at a solution

I started my superposition solution as shown in attachment s8.jpg. I wanted find out if the deflection caused by the distributed load between points A and B is equivilent to the amount of deflection that would occur at point C in the first case. For the second case is the deflection caused by the load occur between points B and C or accross the entire beam? I'm having a difficult time trying to find the best equation to discribe each case.
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 Your response gets me going in the right direction. I'll try what you mentioned and see what I turn up with. If I run into difficulties I'll look for further consultation. Thanks for leading me in the right direction. I was not exactly sure how to find the deflection occuring at C based upon the loadings.

Use virtual work. Set the deflections equal for each case and solve for P. I would guess this is how your instructor wants it to be solved and not just by manipulating existing tables.
 I agree with haynewp

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