A machine can print 12 page in a minute. How long will the machine take to print 5760 pages​?

A machine can print 12 page in a minute. How long will the machine take to print 5760 pages​?

It will take 8 hrs to print 5760 pages.

The machine will take 480 minutes to print 5760 pages.

Here's how we can calculate it:

Divide the total number of pages by the number of pages printed per minute:

5760 pages / 12 pages/minute = 480 minutes

Therefore, the machine will take 480 minutes, or 8 hours (since there are 60 minutes in an hour), to print all 5760 pages.

Alternatively, you could:

Find the reciprocal of the printing rate:

1 / 12 pages/minute = 1/12 minute/page

Multiply the reciprocal by the total number of pages:

1/12 minute/page * 5760 pages = 480 minutes

Both methods arrive at the same answer, so choose whichever one you find easier to understand!

Work Rate Problems in Mathematics

Work rate problems are a classic type of math problem that involve the relationship between three variables: work (amount of work), rate (how much work is done per unit of time), and time (how long it takes to do the work). They can be presented in various contexts, like building a fence, filling a pool, or painting a room.

Here are some key points about work rate problems:

Understanding the formula: The fundamental formula for work rate problems is work = rate * time (often abbreviated as W = R * T). This formula can be rearranged to solve for any of the three variables if you know the other two.

Recognizing the problem type: Work rate problems can be categorized based on the given information:

• Single worker: These problems involve one worker and focus on finding the time to complete a job or the rate at which they work.
• Multiple workers: These problems involve two or more workers working together or separately on the same job. You need to consider the combined rate of working together and individual rates when solving.
• Simultaneous work: These problems involve two or more tasks happening concurrently, like filling and draining a pool simultaneously. You need to account for the rates of both tasks and their combined effect.

Strategies for solving: There are various strategies to approach work rate problems, depending on the specific problem:

• Setting up equations: Write down equations based on the given information and the formula. Use variables to represent unknown quantities and solve the system of equations.
• Drawing diagrams: Visualizing the problem using diagrams can help clarify the relationships between the variables and simplify the solution process.
• Using ratios and proportions: Work rate problems often involve ratios and proportions, especially when dealing with multiple workers or simultaneous tasks. Understanding these concepts can be helpful in solving the problem.