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In heterogeneous distributed systems, such as grids, a resource broker is responsible of automatically selecting resources, and mapping application tasks to them. A crucial aspect of resource broker design, especially in a next commercial exploitation of grid systems, in which economy theories for resource management will be applied, is the support to task mapping based on the fulfillment of quality of service (QoS) constraints. The paper presents an economy-driven mapping heuristic, called time minimization, for mapping and scheduling the tasks assigned to the slaves of a master-slave application in a hierarchical and heterogeneous distributed system. The validity and accuracy of such heuristic are tested by implementing it in a resource broker of a hierarchical grid middleware used for running a real world application.