Sam can paint the walls of a house in 8 hours. What part of the walls can he paint in 6 hours?
Understand the Problem
The question is asking what fraction of the walls Sam can paint in 6 hours, given that he can paint all the walls in 8 hours. This is a ratio problem.
Answer
$\frac{3}{4}$
Answer for screen readers
Sam can paint $\frac{3}{4}$ of the walls in 6 hours.
Steps to Solve
- Determine Sam's painting rate
If Sam can paint all the walls in 8 hours, then his painting rate is $\frac{1}{8}$ of the walls per hour.
- Calculate the fraction of walls painted in 6 hours
To find out what fraction of the walls Sam can paint in 6 hours, multiply his painting rate by the number of hours:
$$ \frac{1}{8} \times 6 = \frac{6}{8} $$
- Simplify the fraction
Simplify the fraction $\frac{6}{8}$ by dividing both the numerator and denominator by their greatest common divisor, which is 2:
$$ \frac{6 \div 2}{8 \div 2} = \frac{3}{4} $$
Sam can paint $\frac{3}{4}$ of the walls in 6 hours.
More Information
This problem is similar to calculating distance traveled when given a speed and time. Here, the "speed" is the rate at which Sam paints, and the "distance" is the fraction of the walls painted.
Tips
A common mistake is to incorrectly set up the initial rate or to forget to simplify the final fraction. Also, some might confuse the given information and perform incorrect operations, such as adding instead of multiplying.
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