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
