• Accueil
  • Math
  • Elaine and gigi can finish cleaning in 2 hours. if...

Elaine and gigi can finish cleaning in 2 hours. if it takes elaine working alone 3 hours longer thain it takes gigi working alone, how many hours will each girl finish the work alone?

Answers

  • Réponse publiée par: pauyonlor

    Gigi= four hours

    Elaine= seven hours

  • Réponse publiée par: Jelanny

    The answer is for Elaine it takes 6 hours and for Gigi 3 hours

    Step-by-step explanation:

    Work problem where

    1/a + 1/b = 1/t

    Where

    a is the time taken by first entity

    b is the time taken by the second entity

    t is the total time the work can be done

    Let

    Elaine = a

    Let Gigi = b

    t is the total time which is 2 hours

    it takes Elaine working alone 3 hours longer than it takes gigi working alone.

    Elaine = Gigi + 3

    a = b + 3

    Substitute the values to 1/a + 1/b = 1/t

    \frac{1}{b+3} +\frac{1}{ b} = \frac{1}{2} \\

    In order to not have b on the denominator : Multiply both sides by\frac{ (b+3)(b)(2)}{b+3} +\frac{ (b+3)(b)(2)}{ b} = \frac{ (b+3)(b)(2)}{2} \\

    Cancel same terms on the numerator and denominator

    2b +(b+3)(2) = (b+3)(b)

    Simplifying

    2b + 2b + 6 = b^{2} +3b

    Combining both terms and transposing

    b^{2} - b - 6 =0

    Factoring

    (b -3 )(b +2) = 0

    Equating zero

    b = 3

    b = -2

    Disregarding the value b = -2 since it is negative

    The value of b therefore is 3 substiture to

    Gigi = b

    Gigi = 3 hours

    Elaine = Gigi + 3

    Elaine = 3+3 = 6 hours

    Therefore the answer is for Elaine it takes 6 hours and for Gigi 3 hours

    Checking

    1/a + 1/b = 1/t

    1/6 +1/3 = 1/2

    #CarryOnLearning

Connaissez-vous la bonne réponse?
Elaine and gigi can finish cleaning in 2 hours. if it takes elaine working alone 3 hours longer thai...