What you will be doing as a MedSpeed Box Truck Medical Driver: What You Will Be Doing as a MedSpeed Box Truck Medical Driver: Safely transport medical supplies, medical equipment, lab specimens, pharmaceuticals, sterile processing instrumentation, healthcare linens, pallets, carts, and other healthcare materials between facilities. Verify that all carts, pallets, and supplies are collected from designated receiving areas and accurately accounted for during pickups and deliveries, immediately reporting any missing, damaged, or unaccounted-for items.