I was given a problem that my book did not explain how to do, so I attempted to figure it out myself. Let me know if my conclusion is fallacious.

Question

Given the reactions
H2O(g) + CO(g) <--> H2(g) + CO2(g), K= 1.6
FeO(s) + CO(g) <--> Fe(s) + CO2(g), K= .67
Find K for the reaction
Fe(s) + H2O(g) <--> FeO(s) + H2(g)

I looked through the numbers and thought this:
In the second reaction, the K value is essentially based on CO(g) and CO2(g), because the pure solids have little/no effect on K. Looking at the reaction I am trying to find, I see that I am essentially finding K for H2O(g) <--> H2(g), because the pure solids do not affect the K value. With this knowledge, I subtracted the K value for [essentially] CO(g)<-->CO2(g) from the K value for H2O(g) + CO(g)<-->H2(g) + CO2(g), leaving me with the K value of H2O(g)<-->H2(g) [or .93]. Does this make sense?

No, it doens't.
H2O(g) + CO(g) <-> H2(g)+CO2(g) K= 1.6
FeO(s) + CO(g) <-> Fe(s)+ CO2(g) K=0.67

Call the first equation #1 and the second #2.
Reverse equation 2. K for that reversed is 1/K = 1/0.67.

Now add equation #1 to the reversed equation #2 to obtain the reaction you want. When adding equations, multiply Ks. So (1/0.67)x 1.6 = K for the final reaction.