book Maths Puzzle Numerical Ability

what is a formuala. and a good explanation going through how you get from one step to another on.. " Cost and Money Problems "... Algebra 1... thank you

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tanA*tanA+(1-sqrt{3})tanA-sqrt{3}=0 An automobile travels 10km at a speed of 100kph, 40km at 80kph and a 3rd diatance at 50kph. If the average velocity for the trip is 70kph, what is the length of the 3rd distance travelled?