Mathematics, 14.07.2019 22:10 Naysa150724

If jackie were to paint her living room alone, it would take 8 hours. her sister patricia could do the job in 9 hours. how long would it take them working together? if needed, submit your answer as a fraction reduced to lowest terms.

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Answer from: smithmariah7426

It takes them to work together for 4 hours and 14 minutes.

Ratio and proportion

A ratio is an ordered pair of numbers a and b, written as a/b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Given

Jackie was to paint her living room alone. It would take 8 hours.

Her sister Patricia could do the job in 9 hours.

To find

How long would it take them to work together?

How to get the solution?

We know the work is inversely proportional to the time. And formula we have

$\rm \dfrac{1}{T_f} = \dfrac{1}{T_1} +\dfrac{1}{T_2}$

We have

$\rm T_1 = 8, \ \ \ and\ \ T_2 = 9$

Then by the formula.

$\rm \dfrac{1}{T_f} = \dfrac{1}{8} +\dfrac{1}{9}\\\\\rm \dfrac{1}{T_f} = \dfrac{8+9}{8*9} \\\\\rm \dfrac{1}{T_f} = \dfrac{17}{72} \\\\T_f \ = \dfrac{72}{17}\\\\T_f \ = 4.24$

Then the time 4.24 will be 4 hours and 14 minutes.

Thus, it takes them to work together for 4 hours and 14 minutes.

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Answer from: myhomeacc32

(72/17) hours

Step-by-step explanation:

Time Jackie would take alone , J = 8 hrs

Time Patricia would take alone , P = 9 hrs

Let the time they will take together be T

use the formula for shared unit rate

$\frac{1}{T}$ = $\frac{1}{J}$ + $\frac{1}{P}$

$\frac{1}{T}$ = $\frac{1}{8}$ + $\frac{1}{9}$

$\frac{1}{T}$ = $\frac{17}{72}$

T = $\frac{72}{17}$ hours (or 4.24 hours)

Answer from: Quest

b: |12 – x| ≤ 0.25

step-by-step explanation:

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

Answer from: Quest

none.

step-by-step explanation:

m1=5

−

b=-1

find the slope and y-intercept of the second equation.

tap for more

m2=0

−

b=-6

compare the slopes

m of the two equations.

m1=5,m2=0

compare the two slopes in the decimal form. if the slopes are equal, then the lines are parallel. if the slopes are not equal, then the lines are not parallel.

m1=5,m2=0

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