Depth · one concept from first principles · step 2 of 4
Working alone, Jaewoo takes days to do of a job, and Seohee takes days to do of the same job. If they work on it together, how many days will it take to finish? (Each person does the same amount of work every day.)
He does 1/4 of the job spread evenly over 5 days, so divide that fraction by 5.
Jaewoo does 1/20 of the job a day.
6.NS.A.1Solve An Easier Related ProblemShe does 2/5 of the job over 2 days, so divide that by 2.
Seohee does 1/5 of the job a day.
7.RP.A.1Solve An Easier Related ProblemWorking together, in one day they finish both shares. Put them over the same denominator and add.
Together they do 1/4 of the job a day.
6.RP.A.3Identify SubproblemsWorking together they finish of the job in a day.
They work at the same time on different parts, so the parts each finishes in a day do not overlap and the two shares add.
Each person does the same amount every day, so one day's share is a fixed size and five of Jaewoo's make the quarter he does in five days.
If a quarter of the job is done each day, four such days finish the whole job.
It takes 4 days.
6.RP.A.3Analyze The UnitsCall the whole job 1, and every worker turns into a fraction you can add.
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The same shape shows up later on the AMC, as Arithmetic Expression Decomposition, Meeting Time with Piecewise Rates. Why the shapes repeat →