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It takes peter 6 hours longer than luis to do a certain job. Together they do it in 4 hours. How long would it take each working alone to do the job?

Sagot :

Luis' work rate: 1/x  (where x is the time it takes for Luis to do the same job.)
Peter's work rate: 1/x+6   (where x+6 is the time it takes for Peter to do the 
                                              same job)
Combined work rate:  1/4    (where 4 is the number of hours it will take if
                                              they work together.)

Equation:
1/x  +  1/x+6 = 1/4

LCD: (4)(x)(x+6)

Multiply each term by (4)(x)(x+6):
1(4)(x)(x+6)  +  1(4)(x)(x+6)  =  1(4)(x)(x+6)
      x                         x+6          4

(4)(x+6) + (4)(x)  = (x)(x+6)
4x + 24 + 4x = x² + 6x
8x + 24 = x² + 6x

Quadratic equation:
x² + 6x - 8x - 24 = 0
x² - 2x - 24 = 0

Solve by factoring:
x² - 2x - 24 = 0
(x - 6) (x + 4) = 0

x - 6 = 0             x + 4 = 0
x = 6                  x = -4 

Choose the positive root, x = 6
Substitute 6 to x in work rate:
Luis: 1/x   ⇒   1/6  ⇒   6 hours
Peter:  1/x+6  ⇒  1/6+6  =  1/12  ⇒    12 hours







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