SOLUTION: On a 570 mile trip Andy averaged 5 miles per hour faster for the last 240 miles than he did for the first 330 miles. The entire trip took 10 hours. How fast did he travel for the

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let x is Andy speed for the first 330 miles,
we can establish the equation as follows:
[330/x] + [240/(x+5)] = 10
(330x +1650 +240x)/x(x+5) = 10
330x +1650 +240x =10x^2 + 50x
(x^2) - 52x - 165 = 0
x=[52+ sqrt(52^2 - 660)]/2 = [52 + sqrt(3364)]/2= [52 + 58]/2
x1= 55 x2=[ 52-58]/2 = -3 negative ( not accepted)
so the solution is x=55 mile/hour in the first 330 miles