Mathematics, 14.12.2019 04:31 fvwk

It takes 23 minutes for 6 people to paint 6 walls. how many minutes does it take 9 people to paint 7 walls?

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For this problem you need to first find a unit rate (rate = 1/time), how fast per minute can 1 person paint a wall?

Once you have this rate you can find how many minutes it takes to do any number of walls with any number of people.

Lets call this unit rate 'r'. Number of people = n, Number of walls = w.
By multiplying the unit rate by 'n', you get the speed n people can paint a wall. Example, if it takes 4 min to paint 1 wall the unit rate = 1/4. The speed for 8 people is 8*(1/4) = 2 walls per minute. Time = 1/rate. So 2 walls per minute = 1/2 min per wall. Now multiply time by w. If there are 10 walls, (1/2)*10 = 5 , It takes 8 people 5 min to paint 10 walls.

The general formula is:
$t = \frac{w}{n*r} \\ \\ r = \frac{w}{n*t}$

Now apply to given problem:
Time = 23 min, n = 6, w = 6
Solve for unit rate 'r'
$r = \frac{6}{6*23} = \frac{1}{23}$
Find time, given
n = 9, w = 7
$t = \frac{7}{9*(1/23)} = \frac{7*23}{9} = 17.89$

it takes 17.89 min or 17 min 53 sec

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

step-by-step explanation:

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