97% of people can not do this problem! Can you? | Summary and Q&A

TL;DR

Alice, Ben, and Chris can complete a job together in 2 hours and 40 minutes.

Key Insights

• ⌛ When solving time and work problems, it is important to consider how many jobs can be completed within a set amount of time.
• 🎭 Converting fractions to improper fractions can simplify calculations and make them easier to perform.
• 🥺 The initial approach of representing the given information as algebraic equations may not always lead to the correct solution.
• 🧑‍🏭 Common factors can be utilized to make calculations simpler and more efficient.
• ⌛ The time it takes to complete one job can be determined by dividing the total time by the number of jobs completed within that time.
• 💦 The solution to the problem indicated that working together may take longer than working individually, highlighting the importance of considering the logical aspects of the problem.
• 💦 Fraction arithmetic is essential in solving time and work problems accurately.

Transcript

good day welcome to the tech maath Channel I'm Josh consider this problem and see if you can solve it Alice and Ben can do a job in 3 hours Alice and Chris can do the same job in 4 hours Ben and Chris can do the same job in 6 hours so how long will the job take if they all work together so pause this video if you'd like to give this problem a try a... Read More

Questions & Answers

Q: How can Alice, Ben, and Chris complete a job together in 2 hours and 40 minutes?

By analyzing how many jobs they can complete within a set amount of time and using algebraic equations, we find that they can complete 4 and 1/2 jobs in 12 hours. Dividing 12 by 4 and 1/2 gives us the time it takes to complete one job, which is 2 hours and 40 minutes.

Q: Why did many people get the incorrect answer when initially solving the problem?

Many people tend to turn the given information into algebraic equations without considering the logic and approach of the problem. This leads to a misconception and incorrect answer.

Q: How did the solution involve common factors?

The solution involved considering the common factors of 3, 4, and 6, which are 12. By determining how many jobs can be completed in 12 hours, we were able to solve the problem more easily.

Q: What is the significance of converting fractions to improper fractions?

Converting fractions to improper fractions allows for easier multiplication and division. In this case, it helped in finding the time it takes to complete one job by dividing 12 by 4 and 1/2.

Summary & Key Takeaways

• Alice and Ben can complete a job in 3 hours, Alice and Chris in 4 hours, and Ben and Chris in 6 hours.

• By considering how many jobs they can complete in 12 hours, we find that they can complete 4 and 1/2 jobs.

• To find the time it takes to complete one job, we divide 12 by 4 and 1/2, resulting in 2 hours and 40 minutes.