Time taken in the morning is 143 minutes, so: \(x^4-2x^3+8x+127=143\)
Rewrite this as; \(x^4-2x^3+8x-16=0\)
This factors as: \((x-2)(x+2)(x^2-2x+4)\)
The only real positive solution is x = 2.
According to the equation you have for the return journey, time taken = \(2^6-8*2^3+2^2-2\times 2+12\rightarrow 12\) minutes!
This doesn't square with heavy traffic!! I think you might have written the second equation incorrectly.
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