Let $R$ be a ring. Take the polynomial ring over $R$

$$R[x_1,\dots, x_n]$$

nonzerodivisors $f,g\in R[x_1,\dots, x_n]$ such that $f$ is a polynomial in the first $k$ indeterminates, $g$ a polynomial in the last $n-k$, $0\le k\le n$.

Suppose both $R[x_1,\dots, x_n]/(f)$ and $R[x_1,\dots, x_n]/(g)$ are flat over $R$.

Is $R[x_1,\dots, x_n]/(f,g)$ still flat over $R$?

Is $Tor_1^{R[x_1,\dots, x_n]}(R[x_1,\dots, x_n]/(f), R[x_1,\dots, x_n]/(g)) = 0$?

If $R$ is a field this is easily seen. Thank you