Brand new to the forum. My apologies if this problem is already posted on the site. I searched a bit but had no luck. 1. The problem statement, all variables and given/known data Problem from Cutnell & Johnson PHYSICS 7th Edition. Chapter 4 - Problem #9 Two forces FA and FB are applied to an object whose mass is 8.0 kg. The larger force is FA. When both forces point due east, the objects acceleration has a magnitude of 0.50 m/s2. However, when FA points due east and FB points due west, the acceleration is 0.40 m/s2, due east. Find (a) the magnitude of FA and (b) the magnitude of FB. 2. Relevant equations F=ma FA + FB = ma1 FA - FB = ma2 3. The attempt at a solution I have the text books solution manual, but don't really understand the solution. Any help would be appreciated. a) Adding equations 1 and 2 gives FA = m (a1 + a2) / 2 = (8.0 kg) (0.50 m/s2 + 0.40 m/s2) / 2 = 3.6 N b) Subtracting equation 2 from equation 1 gives FA = m (a1 - a2) / 2 = (8.0 kg) (0.50 m/s2 + 0.40 m/s2) / 2 = 0.40 N Ok, the final answers make sense when you plug the numbers into the equations. But I'm curious about why the equations are being added and subtracted from each other? In other words, how / why did the book mix the two equations together at get: FA = m (a1 + a2) / 2 FA = m (a1 - a2) / 2 Again, probably just simple algebra that I'm looking over... Thanks for any help!