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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 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.

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Sample set f

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

Step 1:  Let x = length. Then, x 3 = width.

Step 2:  Make a sketch of the rectangle.
A rectangle with the length as
The perimeter of a figure is the total length around the figure.
x + x 3 + x + x 3 = 16 2 x + 2 x 3 = 16 Step 3: 2 x + 2 x 3 = 16. The LCD is 3 . 3 · 2 x + 3 · 2 x 3 = 3 · 16 6 x + 2 x = 48 8 x = 48 x = 6 Check this potential solution . Step 4: 6 + 6 3 + 6 + 6 3 = 16 Is this correct? 6 + 2 + 6 + 2 = 16 Is this correct? 16 = 16 Yes, this is correct. Since  x = 6 , x 3 = 6 3 = 2 Step 5 : The length = 6 cm and the width = 2 cm .

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Practice set f

The width of a rectangle is 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.

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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 3 7 , the result is 2 3 . What is the number?

The number added is 5.

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

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

The number added is 2.

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

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

The number subtracted is 17.

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

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One third of a number added to the reciprocal of number yields 13 6 . What is the number?

x = 1 2 , 6

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Four fifths of a number added to the reciprocal of number yields 81 10 . What is the number?

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

2

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One fourth of a number added to four times the reciprocal of the number yields 10 3 . What is the number?

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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 1 13  hours

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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?

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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

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

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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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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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