In this paper, we obtain lower and upper bounds for the blow-up times to a system of semilinear stochastic partial differential equations given by du1=[(Δ+V1)u1(t,x)+u1m(t,x)+u2n(t,x)]dt+k1u1(t,x)dWt du2=[(Δ+V2)u2(t,x)+u1p(t,x)+u2q(t,x)]dt+k2u2(t,x)dWt where m,n,p,q are constants. Under the assumption that m ≥ n ≥ p ≥ q ≥ 1, the distribution functions of several explosion times are obtained by using explicit solutions of an associated system of random partial differential equations and a formula due to Yor.