We investigate a search and coverage planning problem, where an area of interest has to be explored by a number of vehicles, given a fixed time budget. A good coverage plan has a low probability of a target remaining unobserved. We introduce a formal problem statement, suggest a greedy algorithm to solve the problem, and show experimental results on a number of simulated coverage problems. Our work offers three main contributions. First, we propose an offline planning algorithm that, given some prior knowledge about the target probability in an environment, surveys the area to find the targets as fast as possible while minimizing the energy used. The planning algorithm plans targets to visit and paths to follow for multiple robots, which may have different performance characteristics such as speed, power, and sensor quality. Our second main contribution is to integrate our planning algorithm in the framework of coactive learning, where the system learns the cost function of an in situ human expert, who edits and improves the solutions generated by the system. Our third contribution is an empirical evaluation of the system and a comparison to a state-of-the-art system with provable performance gaurantees on a simulator. The results show that our system yields comparable performance to the state-of-the-art system while respecting hard budget constraints and running orders of magnitude faster.