This paper proposes a vehicle travel speed model to enhance two heuristic algoritihms from previous studies, namely current initial solution (CIS) and different initial customer (DIC). Both algorithms are used to solve a real-life waste collection vehicle routing benchmark problem with dynamic travel speeds. This problem is referred to as Time-Dependent Vehicle Routing Problem (TD-VRP) in previous literature. The benchmark problem consisted of ten sub problems, involving up to 2092 customers. Previous studies solved the benchmark problem using DIC and CIS algorithms with the assumption that the vehicles are travelling with a static speed when collecting the waste. However, in this paper the static speed that was considered in both algorithms were improved by introducing dynamic travel speeds to construct vehicle routes for the waste collection drivers. Compared to previous studies the enhanced CIS and DIC with dynamic travel speeds affected the waste collection problem in terms of the number of vehicles used, the total distance travelled and the total travel time. However, different settings of speed may give different impacts to the solution. The study reveals that with a setting of dynamic speed between 40 mph and 55 mph, DIC is able to reduce two vehicles (from 98 to 96 number of vehicles used), 7.85% of total distance travelled, and 19.10% of total travel time.