I loved our riding mower, so I caint really speak to being bothered by the noise. We had a neighbour though, he had a problem with it. Tried to kill off our grass one time, little prat.
I'd do what the above said and get an MP3 player, but I'd use it to block the noise, not bust your ear drums.
The vacuum though, that did bother me. I found it better if I hummed the same tone as it, made me feel more like I was in control of the noise. You could try that. Also, some of the nicer white noise generators can be taught to cancel certain sounds. May hurt your head a bit though, you're both hearing and not hearing it at the same time.
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Every time you think you've made it idiot proof, someone comes along and invents a better idiot.
?the end of our exploring, will be to arrive where we started, and know the place for the first time. - T.S. Eliot