What is Solving Problems based on Time and Work?

S6-SA1-0140

Grade Level:

Class 10

AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine

Definition

What is it?

Solving problems based on Time and Work involves figuring out how much work can be done in a certain amount of time, or how long it takes to complete a specific task. It helps us understand the relationship between the number of people working, the time they take, and the amount of work completed.

Simple Example

Quick Example

Imagine your school has a wall to paint. If 2 painters can paint it in 10 days, how long will it take 4 painters to paint the same wall? Since more painters mean less time, 4 painters should finish faster.

Worked Example

Step-by-Step

QUESTION: A can do a piece of work in 20 days and B can do the same work in 30 days. In how many days will they complete the work if they work together?

STEP 1: Find the amount of work A does in one day. A's 1-day work = 1/20 of the total work.
---STEP 2: Find the amount of work B does in one day. B's 1-day work = 1/30 of the total work.
---STEP 3: Find the combined work done by A and B in one day. Combined 1-day work = (1/20) + (1/30).
---STEP 4: Find a common denominator for the fractions. The LCM of 20 and 30 is 60.
---STEP 5: Add the fractions: (3/60) + (2/60) = 5/60.
---STEP 6: Simplify the combined 1-day work: 5/60 = 1/12.
---STEP 7: If they complete 1/12 of the work in one day, then they will complete the whole work in the reciprocal of this fraction. Total days = 1 / (1/12) = 12 days.
---ANSWER: They will complete the work together in 12 days.

Why It Matters

Understanding Time and Work is crucial in many fields, from planning construction projects to scheduling rocket launches. Engineers use it to estimate project completion times, while logistics managers apply it to optimize delivery routes and workforce allocation. It's vital for careers in project management, civil engineering, and even event planning.

Common Mistakes

MISTAKE: Adding the number of days directly to find combined time (e.g., A takes 10 days, B takes 15 days, so together they take 10+15 = 25 days). | CORRECTION: Always work with the 'amount of work done in one unit of time' (usually one day or one hour) by each person or machine.

MISTAKE: Assuming more workers always mean proportionally less time, even when efficiency differs. | CORRECTION: Remember that the 'rate of work' (work per unit time) for each individual can be different and must be accounted for.

MISTAKE: Confusing total work with the number of units. | CORRECTION: Think of the 'total work' as '1 unit' or '1 whole job'. This helps in representing fractions of work done correctly.

Practice Questions

Try It Yourself

QUESTION: Ram can finish a task in 15 days. If Shyam is twice as efficient as Ram, how many days will Shyam take to finish the same task? | ANSWER: 7.5 days

QUESTION: A pipe can fill a tank in 10 hours. Another pipe can empty the same tank in 15 hours. If both pipes are opened together, in how many hours will the tank be full? | ANSWER: 30 hours

QUESTION: A, B, and C can complete a work in 10, 12, and 15 days respectively. If A, B, and C start working together, but A leaves after 2 days, how many more days will B and C take to finish the remaining work? | ANSWER: 4 days

MCQ

Quick Quiz

If 5 workers can build a wall in 20 days, how many days will 10 workers take to build the same wall (assuming they work at the same rate)?

40 days

10 days

20 days

5 days

The Correct Answer Is:

If the number of workers doubles, the time taken to complete the same work will be halved, assuming the same efficiency. So, 20 days / 2 = 10 days. Options A, C, and D are incorrect as they don't reflect this inverse relationship.

Real World Connection

In the Real World

In India, companies like L&T (Larsen & Toubro) use Time and Work concepts to plan massive construction projects like metro lines or bridges. They calculate how many workers, machines, and how much time is needed to meet deadlines, ensuring efficient resource allocation and timely completion of these critical infrastructure projects.

Key Vocabulary

Key Terms

EFFICIENCY: The rate at which work is done, or work done per unit of time. | RECIPROCAL: The inverse of a number (e.g., the reciprocal of 1/5 is 5). Used to find total time from 1-day work. | UNIT WORK: The fraction of total work completed in one unit of time (e.g., one day, one hour). | LCM: Least Common Multiple, used to add or subtract fractions of work.

What's Next

What to Learn Next

Next, you can explore advanced problems involving pipes and cisterns, or specific scenarios like 'work and wages' which combine this concept with earnings. Understanding these will further strengthen your problem-solving skills and prepare you for competitive exams.