Card 1 of 20
EasyStudy card 1
Prompt
What represents one whole job?
Answer
\(1\).
MathChapter 14: Rational Expressions
Flashcards
Solving Word Problems Using Rational Equations Flashcards
Twenty concise cards on work rates, combined work, staged jobs, units, and sanity checks.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
If a job takes \(t\) hours, what is the rate?
Answer
\(1/t\) job per hour.
Card 3 of 20
EasyStudy card 3
Prompt
What is the core work formula?
Answer
Work done = rate × time.
Card 4 of 20
EasyStudy card 4
Prompt
How are simultaneous independent work rates combined?
Answer
Add the rates.
Card 5 of 20
EasyStudy card 5
Prompt
Should completion times be added?
Answer
No. Convert times to rates first.
Card 6 of 20
EasyStudy card 6
Prompt
What does \(x/6\) mean in a work equation?
Answer
Work completed in \(x\) hours at \(1/6\) job per hour.
Card 7 of 20
EasyStudy card 7
Prompt
What equation models two workers for \(x\) hours?
Answer
\(x/a+x/b=1\), where \(a,b\) are their solo times.
Card 8 of 20
MediumStudy card 8
Prompt
How is combined time found from combined rate \(r\)?
Answer
Use \(1/r\) for one job.
Card 9 of 20
MediumStudy card 9
Prompt
What sanity check applies to two positive rates?
Answer
Together-time must be less than the fastest solo time.
Card 10 of 20
MediumStudy card 10
Prompt
How much work remains after \(w\) is completed?
Answer
\(1-w\).
Card 11 of 20
MediumStudy card 11
Prompt
How should staged work be modeled?
Answer
Calculate work in each time interval, then add the contributions.
Card 12 of 20
MediumStudy card 12
Prompt
What must happen before mixing minutes and hourly rates?
Answer
Convert all times to one unit.
Card 13 of 20
MediumStudy card 13
Prompt
How many hours is 90 minutes?
Answer
\(3/2\) hours.
Card 14 of 20
MediumStudy card 14
Prompt
What does a rate of \(2/5\) job per hour mean?
Answer
Two fifths of one job is completed each hour.
Card 15 of 20
MediumStudy card 15
Prompt
If the target is three jobs, what replaces the right side 1?
Answer
\(3\).
Card 16 of 20
MediumStudy card 16
Prompt
What answer distinction matters in a staged problem?
Answer
Total elapsed time versus time after another worker joins.
Card 17 of 20
HardStudy card 17
Prompt
Workers take 6 h and 4 h alone. What is their combined rate?
Answer
\(1/6+1/4=5/12\) job per hour.
Card 18 of 20
HardStudy card 18
Prompt
For rates \(1/6\) and \(1/4\), what is together-time?
Answer
\(1/(5/12)=12/5\) hours.
Card 19 of 20
HardStudy card 19
Prompt
Why can a negative time be rejected?
Answer
Time in the work context must be nonnegative; it cannot describe the requested duration.
Card 20 of 20
HardStudy card 20
Prompt
What five checks finish a work-rate solution?
Answer
Target work, stage contributions, units, positivity, and faster-together plausibility.
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