Scheduling is an important task allowing parallel systems to perform efficiently and reliably. For modern computation systems, divisible load is a special type of data which can be divided into arbitrary sizes and independently processed in parallel. Such loads are commonly encountered in applications which are processing a great amount of similar data units. For a multi-task processor, the processor's speed may be time-varying due to the arrival and departure of other background jobs. This paper studies an optimal divisible loads scheduling problem on a single level tree network, whose processing speeds and channel speeds are time-varying. Two recursive algorithms are provided to solve this problem when the arrival and departure times of the background jobs are known a priori and an iterative algorithm is provided to solve the case where such times are not known. Numerical tests and evaluations are performed for these three algorithms under different numbers of background jobs and processors.