# 8.7 Applications  (Page 3/4)

 Page 3 / 4

## Practice set e

It takes person A 4 hours less than person B to complete a certain task. Working together, both can complete the task in $\frac{8}{3}$ hours. How long does it take each person to complete the task working alone?

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

Person A, 4 hr to complete the task; person B, 8 hr complete the task.

## Sample set f

The width of a rectangle is $\frac{1}{3}$ its length. Find the dimensions (length and width) if the perimeter is 16 cm.

Step 1:  Let $x$ = length. Then, $\frac{x}{3}=$ width.

Step 2:  Make a sketch of the rectangle.

The perimeter of a figure is the total length around the figure.
$\begin{array}{l}\begin{array}{ccccccc}\hfill & \hfill & x+\frac{x}{3}+x+\frac{x}{3}\hfill & =\hfill & 16\hfill & \hfill & \hfill \\ \hfill & \hfill & \hfill 2x+\frac{2x}{3}& =\hfill & 16\hfill & \hfill & \hfill \\ \text{Step\hspace{0.17em}3:}\hfill & \hfill & \hfill 2x+\frac{2x}{3}& =\hfill & 16.\hfill & \hfill & \text{The\hspace{0.17em}LCD\hspace{0.17em}is\hspace{0.17em}3}\text{.}\hfill \\ \hfill & \hfill & 3\text{\hspace{0.17em}}·\text{\hspace{0.17em}}2x+3\text{\hspace{0.17em}}·\text{\hspace{0.17em}}\frac{2x}{3}\hfill & =\hfill & 3\text{\hspace{0.17em}}·\text{\hspace{0.17em}}16\hfill & \hfill & \hfill \\ \hfill & \hfill & \hfill 6x+2x& =\hfill & 48\hfill & \hfill & \hfill \\ \hfill & \hfill & \hfill 8x& =\hfill & 48\hfill & \hfill & \hfill \\ \hfill & \hfill & \hfill x& =\hfill & 6\hfill & \hfill & \text{Check\hspace{0.17em}this\hspace{0.17em}potential\hspace{0.17em}solution}\text{.}\hfill \\ \text{Step\hspace{0.17em}4:}\hfill & \hfill & 6+\frac{6}{3}+6+\frac{6}{3}\hfill & =\hfill & 16\hfill & \hfill & \text{Is\hspace{0.17em}this\hspace{0.17em}correct?}\hfill \\ \hfill & \hfill & 6+2+6+2\hfill & =\hfill & 16\hfill & \hfill & \text{Is\hspace{0.17em}this\hspace{0.17em}correct?}\hfill \\ \hfill & \hfill & \hfill 16& =\hfill & 16\hfill & \hfill & \text{Yes,\hspace{0.17em}this\hspace{0.17em}is\hspace{0.17em}correct.}\hfill \\ \hfill & \hfill & \hfill \text{Since\hspace{0.17em}}x& =\hfill & 6,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{x}{3}=\frac{6}{3}=2\hfill & \hfill & \hfill \end{array}\hfill \\ \text{Step\hspace{0.17em}5}:\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{The\hspace{0.17em}length\hspace{0.17em}=\hspace{0.17em}6\hspace{0.17em}cm\hspace{0.17em}and\hspace{0.17em}the\hspace{0.17em}width\hspace{0.17em}=\hspace{0.17em}2\hspace{0.17em}cm}\text{.}\hfill \end{array}$

## Practice set f

The width of a rectangle is $\frac{1}{12}$ its length. Find the dimensions (length and width) if the perimeter is 78 feet.

Step 1:

Step 2:

Step 3:

Step 4:

Step 5:

length = 36 ft, width = 3 ft.

## Exercises

For the following problems, solve using the five-step method.

When the same number is added to both the numerator and denominator of the fraction $\frac{3}{7},$ the result is $\frac{2}{3}.$ What is the number?

When the same number is added to both the numerator and denominator of the fraction $\frac{5}{8},$ the result is $\frac{3}{4}.$ What is the number?

When the same number is added to both the numerator and denominator of the fraction $\frac{3}{8},$ the result is $\frac{1}{6}.$ What is the number?

The number added is $-2.$

When the same number is added to both the numerator and denominator of the fraction $\frac{7}{9},$ the result is $\frac{2}{3}.$ What is the number?

When the same number is subtracted from both the numerator and denominator of $\frac{1}{10},$ the result is $\frac{2}{3}.$ What is the number?

The number subtracted is $-17.$

When the same number is subtracted from both the numerator and denominator of $\frac{3}{4},$ the result is $\frac{5}{6}.$ What is the number?

One third of a number added to the reciprocal of number yields $\frac{13}{6}.$ What is the number?

$x=\frac{1}{2},6$

Four fifths of a number added to the reciprocal of number yields $\frac{81}{10}.$ What is the number?

One half of a number added to twice the reciprocal of the number yields 2. What is the number?

2

One fourth of a number added to four times the reciprocal of the number yields $\frac{-10}{3}.$ What is the number?

One inlet pipe can fill a tank in 8 hours. Another inlet pipe can fill the tank in 5 hours. How long does it take both pipes working together to fill the tank?

$3\frac{1}{13}\text{\hspace{0.17em}hours}$

One pipe can drain a pool in 12 hours. Another pipe can drain the pool in 15 hours. How long does it take both pipes working together to drain the pool?

A faucet can fill a bathroom sink in 1 minute. The drain can empty the sink in 2 minutes. If both the faucet and drain are open, how long will it take to fill the sink?

two minutes

A faucet can fill a bathtub in $6\frac{1}{2}$ minutes. The drain can empty the tub in $8\frac{1}{3}$ minutes. If both the faucet and drain are open, how long will it take to fill the bathtub?

An inlet pipe can fill a tank in 5 hours. An outlet pipe can empty the tank in 4 hours. If both pipes are open, can the tank be filled? Explain.

No. $x=-20$ hours.

a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
im not good at math so would this help me
how did I we'll learn this
f(x)= 2|x+5| find f(-6)
f(n)= 2n + 1
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
Got questions? Join the online conversation and get instant answers!