I am an Economist subscriber and just download the audio edition each week. I listen to it when doing other tasks that don't require 100% mental focus such as housework and am usually able to complete each week's issue before the next one releases. I am not absorbing the content as well as if I were to sit down and read each issue, but this is a reasonable tradeoff for me.

They also have an android/iphone app for subscribers, but I've had a lot of issues with playing audio through it and find it much easier to simply download each week's .zip file of .mp3's and play them with my audio player of choice.