How to solve this algebra 2 word problem?

Time = Distance/Speed .. or in this case:
Time = (Distance1 / Speed1) + (Distance2/Speed2)

3 = 42/(x+6) + 55/x

3 = (42x)/(x^2 + 6x)  + (55x + 330)/(x^2 + 6x)
 
3 = (97x + 330) / (x^2 + 6x)

97x + 330 = 3x^2 + 18x

3x^2 -79x - 330 = 0

and the roots are x = -3.66 (rejected) or:

x = 30 miles per hour for the last 55 miles.
x + 6 = 36 miles per hour for the first 42 miles.

The last 55 miles were driven at x mph so for first 42 miles the speed was x+6
so 42/(x+6) + 55/x = 3
solving we get x = 30 and 36 mph

Let x is the speed they drove in the first 42 miles.
then the speed for the last 55miles is (x - 6)

Time for the first 42 miles is 42/x
Time for the last 55 miles is 55/(x - 6)

Total time is 3 hours
So you come up with this equation:

42/x + 55/(x - 6) = 3.
Common denominator is x(x - 6)

42(x - 6) + 55x = 3x(x - 6)
Expand all terms

42x - 252 + 55x = 3x^2 - 18x
Combine the like term and move all term to 1 side of the "="

3x^2 - 115x + 252 = 0
(x - 36)(3x - 7) = 0

x = 7/3 <=== Too small so it is not the answer

x = 36 <=====This is the answer

The first 42 miles they drove 36 miles per hour
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testing

42/36 + 55/(36 - 6)
= 7/6 + 11/6 = 18/6 = 3.
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