Problem
Set the whole job to 1 and write a day's work as a fraction
Two people each do a known fraction of a job in a known number of days. We need how many days they take working together.
RatiosNumber system
Your answer
How to solve
Strategy Identify Subproblems — Nothing here can be added while the two people are described over different numbers of days. Call the whole job 1, reduce each person to a per-day fraction, and the two become addable.
1STEP 1
Find Jaewoo's daily share
He does 1/4 of the job spread evenly over 5 days, so divide that fraction by 5.
1/4 ÷ 5 = 1/20
Jaewoo does 1/20 of the job a day.
6.NS.A.1Solve An Easier Related Problem2STEP 2
Find Seohee's daily share
She does 2/5 of the job over 2 days, so divide that by 2.
2/5 ÷ 2 = 1/5
Seohee does 1/5 of the job a day.
7.RP.A.1Solve An Easier Related Problem3STEP 3
Add the two daily shares
Working together, in one day they finish both shares. Put them over the same denominator and add.
1/20 + 4/20 = 5/20 = 1/4
Together they do 1/4 of the job a day.
6.RP.A.3Identify SubproblemsWorking together they finish of the job in a day.
Why?
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.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Why?
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.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
4STEP 4
Read back the number of days
If a quarter of the job is done each day, four such days finish the whole job.
1 ÷ 1/4 = 4
It takes 4 days.
6.RP.A.3Analyze The UnitsAnswer
4 days
Check the total: 4 × 1/4 = 1, the whole job.
Takeaway
Call the whole job 1, and every worker turns into a fraction you can add.
- Find Jaewoo's daily share
- Find Seohee's daily share
- Add the two daily shares
- Read back the number of days