Find the velocity constant K given the speed
You are really confusing yourself. The problem is very simple. First of all, remove the fact that the rate of reaction depends on all reactants from your mind. It is not the case. Sometimes, even though multiple reactants are involved, only some of them actually matter when we need to find the rate. Let me explain it without chemistry.

Consider a factory where a car is made. The first level makes the engine in 1 hour. The second level makes the tyres in 1 hour. The third level makes the rest of the parts in 1 hour. The fourth level puts them all together in 1 day. Now, even though all the 4 levels are involved in the process, it is the slowest level (level IV) that determines the rate of the process because the rest of the levels can keep sending the parts, but the finished car won't exit the factory unless level IV puts them all together. This is the case with chemical reactions too! The slowest step decides the order and rate of the reaction.

Now, back to the problem. Since they have given that the reaction follows first order kinetics in $[A]$, the rate law can be written as $R=k[A]$. After a little bit of integration and other stuff, we have the equation, $k=\frac{ln(2)}{t _{1/2}}$ , where $t _{1/2}$ is the half-life, i.e. time taken for concentration (actually, it's no. of molecules) of reactant to become half its original value. In this problem, $t _{1/2}$=10.0 seconds. Substitute and find the answer.