Long term evolution (LTE) wireless local area networks (WLAN) aggregation (LWA) has recently emerged as a promising technology for mobile data offloading. In this paper, non-collocated LWA scenario is considered in which the LTE evolved Node B (eNB) is connected to WLAN infrastructure through wireless backhaul link adopting adaptive modulation. The delay over the wireless backhaul is analyzed and its effect on the offloading and aggregation processes in LWA is investigated. Based on the delay analysis of the backhaul, a scheduling technique with embedded mode selection criteria for LWA is proposed. The technique is designed to maximize the amount of data traffic that can be offloaded to WLAN while considering the user's service time constraint and hence gain the maximum benefit from the cost effective WiFi networks. Simulation results show that using adaptive modulation on the backhaul link helps in reducing the user's experienced delay over the WLAN path and hence increasing the opportunity to offload a larger amount of data from LTE. Also, the impact of different load and the number of WLAN users on the LWA performance at different service time constraints is analyzed and concluded.