What is the minimum strength training needed when training f

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I am starting out training for my 1st 1/2 marathon. In the past I incorporated about a 50/50 split btwn short runs and strength.

Now I am running way more and on with a busy life, I don't have time to still do as much strength training. How much is the minimum amount needed?

I am looking at the 10min Tony Horton workouts...he has 3 of them Total body, legs, and abs. I already do the yoga/stretching one after runs. So is doing each workout 1x a week enough (total of 3 workouts a week)? I am not looking to be an elite runner...just want to make sure I have at least some muscle tone.

Thanks!