problem on time and work solved as a quadratic

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--------------------------------------------------------------------- algebraPerson A takes 6 days less than the time taken by the person B to finish a particular piece of work. If both A and B work together , they can finish it in 4 days. Find the time that B would take to finish this work by himself Let x be number of days taken by person B to finish the work by himself therefore A takes (x-6) days to finish the work by himself. therefore [1 / (x-6)] and [1/x] are the part of the work finished by A and B respectively in a single day Working together they require 4 days to finish the work therefore 4{ [1 / (x-6)] + [1/x] }
= 14{ x + (x-6)}/{x(x-6)} =1 4{ 2x -6)}/{x(x-6)} =1 4{ 2x -6)} = {x(x-6)}8x-24 = (x^2) -6x (x^2) - 14x + 24 = 0 factorising (x-2)(x-12) = 0 x=2 or x=12 if x = 2, y =2-6 = -4 is negative which is not possible therefore x = 12 days. -------------- form a quadratic equation whose roots are 3 and 4 sum of the roots S = 3 +4 =7 product of the roots P = 3*4 = 12 required quadratic equation is (x^2) -Sx+P=0 (x^2)
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