A note on tunnel number of composite knots

Let K be a knot in a sphere S3. We denote by t(K) the tunnel number of K. For two knots K1 and K2, we denote by K1♯K2 the connected sum of K1 and K2. In this paper, we will prove that if one of K1 and K2 has high distance while the other has distance at least 3 then t(K1♯K2)=t(K1)+t(K2)+1.