Drought escape and dehydration avoidance represent alternative strategies for drought adaptation in annual crops. The mechanisms underlying these two strategies are reported to have a negative correlation, suggesting a trade-off. We conducted a quantitative trait locus (QTL) analysis of flowering time and root mass, traits representing each strategy, in Brassica napus to understand if a trade-off exists and what the genetic basis might be. Our field experiment used a genotyped population of doubled haploid lines and included both irrigated and rainfed treatments, allowing analysis of plasticity in each trait. We found strong genetic correlations among all traits, suggesting a trade-off among traits may exist. Summing across traits and treatments we found 20 QTLs, but many of these co-localized to two major QTLs, providing evidence that the trade-off is genetically constrained. To understand the mechanistic relationship between root mass, flowering time, and QTLs, we analysed the data by conditioning upon correlated traits. Our results suggest a causal model where such QTLs affect root mass directly as well as through their impacts on flowering time. Additionally, we used draft Brassica genomes to identify orthologues of well characterized Arabidopsis thaliana flowering time genes as candidate genes. This research provides valuable clues to breeding for drought adaptation as it is the first to analyse the inheritance of the root system in B. napus in relation to drought.