Time & Work explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
Step 1
Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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Time and work problems compare how fast people or machines complete a task.
The key idea is work rate. Work rate means the part of work completed in one unit of time.
This topic is used in jobs, machines, filling tanks, group work, and planning.
If a person completes a job in 5 days, then in 1 day the person completes of the job.
When people work together, their rates are added, not their total times.
Total work is often treated as 1 whole job.
If someone leaves or joins, split the work into time parts and calculate each part separately.
Meaning: Work rate is how much work is done in one unit of time.
Definition: If a job is completed in n days, onay wor.
If A finishes a job in 4 days, A does of the job per day.
Meaning: Combined work rate is found by adding individual rates.
Definition: Together ratate of ate of B.
If A does per day and B does per day, together they do per day.
Meaning: Time is found from the total work and rate.
Definition: Time takeotal worork rate.
If together rate is job per day, they finish 1 job in 2 days.
Meaning: The working rate changes when someone joins or leaves.
Definition: Split the problem into parts where the same people are working together.
Find work done before the change. Then find remaining work with the new rate.
Easy
Question: A completes a job in 5 days. What part does A complete in 1 day?
Medium
Question: A finishes a job in 6 days and B in 3 days. How long do they take together?
Exam-level
Question: A can finish work in 10 days. B can finish it in 15 days. They work together for 3 days. What part is left?
Adding times directly
Why it happens: The problem gives days, so days are added.
Correct approach: Convert time to work rate first.
Forgetting total work is one whole
Why it happens: No physical amount is given.
Correct approach: Treat the full job as 1.
Not splitting joieave problems
Why it happens: One rate is used for the whole problem.
Correct approach: Split the timeline whenever the group changes.
Why do we use 1 for total work?
Because the full job is treated as one whole.
Should I add the number of days?
No. Add work rates, not total times.
What if one pipe empties a tank?
Then its rate is subtracted because it removes work instead of adding it.
Practise the same concept from this article. Your student profile may guide entitlement and follop recommendations, but it does not replace this concept.