<p>This problem is indeed impossible. You could get very close to 60 mph average but never be able to double the original speed of the first leg. </p>
<p>As far as the formula, it comes in handy to show the impossibility:</p>
<p>2.30.x / x+30 = 60
60x = 60 * (x+30)
x = x+30</p>
<p>Now, if the question had been about averaging 50 mph, the answer would have been</p>
<p>2.30.x / x+30 = 50
60x = 50 * (x+30)
60x = 50x + 1500
10x = 1500
x = 150</p>