Strain rate and temperature dependence of the tensile strength of single-wall carbon nanotubes has been investigated with molecular dynamics simulations. The tensile failure or yield strain is found to be strongly dependent on the temperature and strain rate. A transition state theory based predictive model is developed for the tensile failure of nanotubes. Based on the parameters fitted from high-strain rate and temperature dependent molecular dynamics simulations, the model predicts that a defect free micrometer long single-wall nanotube at 300 K, stretched with a strain rate of 1%/hour, fails at about 9 plus or minus 1% tensile strain. This is in good agreement with recent experimental findings.