The basic approach that you are describing sounds like inverse efficiency scores (e.g., see Townsend and Ashby, 1978,1983), which are measured as
$$\frac{r}{1-e} = \frac{r}{c}$$
where $r$ is reaction time, $e$ is proportion error, and $c$ is proportion correct. John Christie provides a critique of inverse efficiency scores here or see the discussion in Bruyer and Brysbaert (2011).
This existing question on "How to analyze reaction times and accuracy together?" hopefully answers your question. The answers there generally advocate more sophisticated approaches for combining reaction time and accuracy such as the Linear Ballistic Accumulator Model and Ratcliff's diffusion model.
References
- Bruyer, R. & Brysbaert, M. (2011). Combining Speed and Accuracy in Cognitive Psychology: Is the Inverse Efficiency Score (IES) a Better Dependent Variable than the Mean Reaction Time (RT) and the Percentage Of Errors (PE)?. Psychologica Belgica, 51, 5-13. PDF
- Townsend, J.T., & Ashby, F.G. (1978). Methods of modeling capacity in simple
processing systems. In J. Castellan & F. Restle (Eds.), Cognitive theory. Vol. 3.
(pp. 200-239). Hillsdale, N.J.: Erlbaum.
- Townsend, J.T., & Ashby, F.G. (1983). Stochastic modeling of elementary psychological processes. Cambridge: Cambridge University Press.