# Question #86523

Apr 3, 2017

2.4 or 2 2/5 of an hour.

#### Explanation:

Mary can clean 1/4 of the classroom in one hour

$\frac{1}{2} / \frac{2}{1}$ can be simplified by multiplying both the denominator and numerator by 1/2 this results in

$\frac{\frac{1}{2} \times \frac{1}{2}}{\frac{2}{1} \times \frac{1}{2}}$ The denominator becomes 1 leaving

$n t \frac{1}{2} \times \frac{1}{2} = 1 / 4$

Suzzie can clean 1/6 of the classroom in one hour.
g
$\frac{1}{3} / \frac{1}{2}$ can be simplified by multiplying both the denominator and numerator by 1/2 this results in

$\frac{\frac{1}{3} \times \frac{1}{2}}{\frac{2}{1} \times \frac{1}{2}}$ The denominator becomes 1 leaving

$\frac{1}{3} \times \frac{1}{2} = \frac{1}{6}$

The amount of the class work that can be cleaned in one hour by both working together can be expressed in this equation.

$\frac{1}{4} + \frac{1}{6} = \frac{1}{T}$ where T is the total amount of time needed to clean the classroom

to solve for T multiply by the LCM of all the denominators

The LCM is 12 T so

12 T( 1/4 + 1/6 = 1/T) This gives

$3 T + 2 T = 12$ Adding common terms

$5 T = 12$ Divide both sides by 5

$5 \frac{T}{5} = \frac{12}{5}$ this results in

T = 2 2/5