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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?
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Step 2:
Step 3:
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Step 5:
Person A, 4 hr to complete the task; person B, 8 hr complete the task.
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.
$\begin{array}{l}\begin{array}{ccccccc}\hfill & \hfill & x+\frac{x}{3}+x+\frac{x}{3}\hfill & =\hfill & 16\hfill & \hfill & \hfill \\ \hfill & \hfill & \hfill 2x+\frac{2x}{3}& =\hfill & 16\hfill & \hfill & \hfill \\ \text{Step\hspace{0.17em}3:}\hfill & \hfill & \hfill 2x+\frac{2x}{3}& =\hfill & 16.\hfill & \hfill & \text{The\hspace{0.17em}LCD\hspace{0.17em}is\hspace{0.17em}3}\text{.}\hfill \\ \hfill & \hfill & 3\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}2x+3\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}\frac{2x}{3}\hfill & =\hfill & 3\text{\hspace{0.17em}}\xb7\text{\hspace{0.17em}}16\hfill & \hfill & \hfill \\ \hfill & \hfill & \hfill 6x+2x& =\hfill & 48\hfill & \hfill & \hfill \\ \hfill & \hfill & \hfill 8x& =\hfill & 48\hfill & \hfill & \hfill \\ \hfill & \hfill & \hfill x& =\hfill & 6\hfill & \hfill & \text{Check\hspace{0.17em}this\hspace{0.17em}potential\hspace{0.17em}solution}\text{.}\hfill \\ \text{Step\hspace{0.17em}4:}\hfill & \hfill & 6+\frac{6}{3}+6+\frac{6}{3}\hfill & =\hfill & 16\hfill & \hfill & \text{Is\hspace{0.17em}this\hspace{0.17em}correct?}\hfill \\ \hfill & \hfill & 6+2+6+2\hfill & =\hfill & 16\hfill & \hfill & \text{Is\hspace{0.17em}this\hspace{0.17em}correct?}\hfill \\ \hfill & \hfill & \hfill 16& =\hfill & 16\hfill & \hfill & \text{Yes,\hspace{0.17em}this\hspace{0.17em}is\hspace{0.17em}correct.}\hfill \\ \hfill & \hfill & \hfill \text{Since\hspace{0.17em}}x& =\hfill & 6,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{x}{3}=\frac{6}{3}=2\hfill & \hfill & \hfill \end{array}\hfill \\ \text{Step\hspace{0.17em}5}:\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{The\hspace{0.17em}length\hspace{0.17em}=\hspace{0.17em}6\hspace{0.17em}cm\hspace{0.17em}and\hspace{0.17em}the\hspace{0.17em}width\hspace{0.17em}=\hspace{0.17em}2\hspace{0.17em}cm}\text{.}\hfill \end{array}$
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.
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?
The number added is 5.
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.
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