We report accurate quantum mechanical reaction probabilities, rate constants, and activation energies for collinear T+HD→TH+D on an accurate potential energy surface. We also report approximate calculations by conventional transition state theory, the unified statistical model, and three versions of variational transition state theory. We include tunneling contributions by two quantum mechanical and three semiclassical methods based on a vibrationally adiabatic treatment of reaction in the ground state. The most accurate approximate calculations for temperatures up to 1500 K are the improved canonical variational theory with Marcus-Coltrin path vibrationally adiabatic ground state (MCPVAG) transmission coefficient and the microcanonical variational theory with MCPVAG transmission coefficient. These two theories and the unified statistical theory with MCPVAG transmission coefficient are accurate within 41% for 400-2400 K but underestimate the rate constant by factors of 2.0 and 2.6 at 300 and 200 K, respectively. The two most accurate approximate theories overestimate the energy of activation for 300-1000 K by 0.46 kcal/mole. The unified statistical model with MCPVAG transmission coefficient produces slightly less accurate rate constants for 600-1500 K and more accurate ones at 2400 K. It overestimates the activation energy for 300-1000 K by only 0.40 kcal/mole.