# 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: 1

## Answers

Elaine and gigi can finish cleaning in 2 hours. if it takes elaine working alone 3 hours longer thai...

Gigi= four hours

Elaine= seven hours

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

In order to not have b on the denominator : Multiply both sides by

Cancel same terms on the numerator and denominator

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

Simplifying

Combining both terms and transposing

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

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