Math Problem Statement
If 2 painters can paint 2 rooms in 2 hours how many painter is needed to paint 18 rooms in 6 hours?
Use algebraic expression
Solution
Let's break down the problem using algebraic expressions.
Step 1: Determine the rate of painting.
Given:
- 2 painters can paint 2 rooms in 2 hours.
First, calculate the rate at which the painters work together.
The rate of painting for the 2 painters is:
Since this rate is for 2 painters, the rate for 1 painter is:
Step 2: Set up the equation for the required number of painters.
Let be the number of painters needed to paint 18 rooms in 6 hours.
The total work that needs to be done is 18 rooms, and they have 6 hours to do it. The rate at which these painters need to work together is:
Step 3: Set up the equation.
We know that 1 painter can paint room per hour, so painters can paint:
We want this to equal the required rate of 3 rooms per hour:
Step 4: Solve for .
Multiply both sides of the equation by 2 to solve for :
Final Answer:
You need 6 painters to paint 18 rooms in 6 hours.
Would you like further details or have any questions? Here are 5 related questions you might find useful:
- How would the number of painters change if you had more or fewer hours available?
- What if the rate of painting for one painter was different—how would that affect the result?
- Can you express the relationship between the number of rooms, painters, and time as a general formula?
- What assumptions are we making in this problem?
- How would you calculate the time needed to paint a different number of rooms with a fixed number of painters?
Tip: Always double-check the units you're working with when setting up and solving algebraic expressions, especially in word problems!
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Math Problem Analysis
Mathematical Concepts
Rate of Work
Proportional Relationships
Algebraic Equations
Formulas
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Theorems
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Suitable Grade Level
Grades 6-8
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