Question

Fran can clean the garage in 3hours, but it takes Angie 4hours to do the same job. How long would it take them to clean the garage if they worked together?

Answer 1

Fran can clean $\frac{1}{3}$ of garage in one hour. Angie can clean $\frac{1}{4}$ of garage in one hour. Working together they can clean
$\dfrac{1}{3}+\dfrac{1}{4}=\dfrac{7}{12}$ of the garage in one hour.
Whole garage will be cleaned in $\frac{12}{7}=1\frac{5}{7}$ hours. (approx. 1 hour and 43 minutes)

Answer 2

Fractions are numbers that have both a numerator and a denominator.

To solve this question, we would require the use of fractions.

it will take both of them $1\frac{5}{7}$ hours to clean the garage if they worked together.

The time it takes Fran to clean the garage = 3 hours

This means Fran will clean 1/3 of the garage in 1 hour.

The time it takes Angle  to clean the garage = 4 hours

This means Angle will clean 1/4 of the garage in 1 hour.

Let's represent the time it takes for them to clean the garage together as = T

Hence:

1/T = 1/3 + 1/4

Lowest common denominatior (3, 4) = 12

1/T = 4 + 3 / 12

1/T = 7/12

This can be rewritten as:

T = 12/7

T = $1\frac{5}{7}$ hours

Therefore, it will take both of them $1\frac{5}{7}$ hours to clean the garage if they worked together.

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