In this paper, we investigate the following quasilinear reaction diffusion equations {(b(u))t = r▽·(ρ(∣▽u∣2)▽u)+c(x)f(u) in Ω × (0,t*), ∂u/∂v = 0 on ∂Ω × (0,t*) u(x,0)=u0=u0(x)≤0 inΩí Here Ω is a bounded domain in Rn (n ≤ 2) with smooth boundary ∂Ω. Weighted nonlocal source satisfies c(x)f(u(x, t)) ≥ a1 + a2 (u(x, t))p(∫Ω(u(x, t))α dx)m, where a2, p, α are some positive constants and a1,m are some nonnegative constants. We make use of a differential inequality technique and Sobolev inequality to obtain a lower bound for the blow-up time of the solution. In addition, an upper bound for the blow-up time is also derived. [ABSTRACT FROM AUTHOR]