A Step-by-Step Guide to Solving Problems Involving Rates in Mathematics

A=RTFor problems with multiple workers or machines, create rates for each one and then add the rates.

In mathematics, when dealing with problems involving multiple workers or machines, we often use the concept of rates to analyze the situation

In mathematics, when dealing with problems involving multiple workers or machines, we often use the concept of rates to analyze the situation. The formula you mentioned, A = RT, is a common formula used to solve such problems.

Here’s a breakdown of the formula:

A – This represents the amount of work or task that needs to be completed. It could be measured in units of work, distance, or any other relevant quantity.

R – This represents the rate at which a worker or machine can complete the task. The rate is usually measured in units of work per unit of time (e.g., tasks per hour, miles per hour).

T – This represents the time it takes to complete the task. It is measured in the same units as the rate (e.g., hours, minutes).

Let’s consider an example to understand the application of this formula:

Suppose you have two workers, Anna and Ben, who are painting a room together. Anna can paint 2 square meters per hour, and Ben can paint 3 square meters per hour. You are asked to find out how long it will take for them to paint a room that is 20 square meters in area.

To solve this problem, we can set up two equations representing the rates of each worker:

Anna’s rate: Aᴀ = 2 square meters per hour
Ben’s rate: Aʙ = 3 square meters per hour

We can then add these rates to find the combined rate of both workers:

Combined rate: Aᴀʙ = Aᴀ + Aʙ = 2 + 3 = 5 square meters per hour

Now, we can use the formula A = RT, where A is the total area to be painted (20 square meters) and R is the combined rate (5 square meters per hour):

20 = 5T

To find the time it will take for both workers to paint the room, we rearrange the equation:

T = 20/5 = 4 hours

Therefore, it will take Anna and Ben together 4 hours to paint the room.

By creating rates for each worker (or machine) and combining them, we can efficiently solve problems involving multiple workers or machines. This approach allows us to analyze the situation in terms of how much work can be done in a given unit of time, making problem-solving more systematic and manageable.

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