Algebra help! (word problem)?

Question

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 Andy travel for the first 330 miles?

Answer 1

Let's call his earlier (slower) rate x. You then have:

330 / x + 240 / (x + 5) = 10

Multiply by x(x+5) to get rid of the denominators, and divide by 10:

33(x+5) + 24(x) = 1(x)(x+5)
33x + 165 + 24x = x^2 + 5x
x^2 - 52x - 165 = 0
x = (52 +/- sqrt(52^2 + 4*165))/2
x = (52 +/- 58) / 2
x = 55, x = -3

Discard the negative answer, and the remaining one is 55 mph.

Checking the answer:

330 mi @ 55mph = 6 hours
240 mi @ (55+5) mph = 4 hours
Total = 10 hours

Answer 2

330/x + 240/(x+5) = 10
33(x+5) + 24x=x^2 + 5x
x^2 -52x -165 = 0
x^2 -55x + 3x -165 = 0

x= 55 or -3

So 55 miles/hr