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Lesson 83: Algebra I #3.4c, Use equations to solve Work or Rate problems

Algebra 1
Lesson 83: Algebra I #3.4c, Use equations to solve Work or Rate problems
Algebra I #3.4c, Use equations to solve Work or Rate problems
Lesson 83: Algebra I #3.4c, Use equations to solve Work or Rate problems

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Question 1 of 10

1. Question

When solving a joint work rate problem involving two people working together, what is the first key step after identifying the individual completion times?

Multiply the two individual times together to get the total combined rate.
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Subtract the smaller individual time from the larger individual time.
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Express the work completed by each person in one unit of time as a fraction.
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Set the variable equal to the sum of the individual days.
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Question 2 of 10

2. Question

If Person A completes a job alone in 4 hours and Person B completes the same job alone in 6 hours, which equation represents them working together for h hours?

(6 – 4)h = 1
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\frac{1}{4} + \frac{1}{6} = h
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(\frac{1}{4} + \frac{1}{6})h = 1
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(4 + 6)h = 1
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Question 3 of 10

3. Question

In the lesson’s example, Bob takes 3 days and Dave takes 5 days to build a go-kart. What is their combined fraction of work done in a single day?

1/15
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15/8
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8/15
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2/8
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Question 4 of 10

4. Question

To solve the work equation (8/15)x = 1 for the variable x, which algebraic operation should be performed?

Subtract 8/15 from both sides.
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Add 15/8 to both sides.
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Multiply both sides by the reciprocal, 15/8.
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Divide both sides by 15.
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Question 5 of 10

5. Question

What was the final calculated time for Bob and Dave to build the go-kart together?

2.500 days
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4.000 days
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0.533 days
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1.875 days
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Question 6 of 10

6. Question

Why does the lesson emphasize carefully identifying what a word problem is asking for, especially in multi-step interest problems?

Because account balances can only be solved using work rate formulas.
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Because interest calculations require dividing by 100 twice.
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Because interest is always expressed as a percentage rather than a whole number.
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Because calculating interest is only an intermediate step; the problem may ask for total account balance.
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Question 7 of 10

7. Question

How should a 2% interest rate be written as a decimal coefficient in an equation?

0.02
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0.002
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0.2
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2.0
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Question 8 of 10

8. Question

Lisa has $500 in her savings account. After the bank adds 2% interest, what is the total balance in her account?

$510
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$520
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$502
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$10
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Question 9 of 10

9. Question

According to the lesson, what is the very first step when approaching any algebraic word problem?

Set the equation equal to zero.
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Determine exactly what the problem is asking for.
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Perform quick mental calculation without writing a variable.
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Immediately write down fractions for each number in the text.
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Question 10 of 10

10. Question

In a work rate problem where Person A takes 3 days alone and Person B takes 5 days alone, why must the combined time be less than 3 days?

Because working together allows them to complete the job faster than the fastest individual working alone.
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Because interest accumulates daily.
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Because fractional rates must always yield decimal values below 1.
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Because work rate problems always divide individual times by two.
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