It takes Mike 18 minutes to finish reading 4 pages of a book. How long does it take Mike to finish reading 30 pages?
Understand the Problem
The question is asking how long it would take Mike to read 30 pages of a book given that he takes 18 minutes to read 4 pages. This involves setting up a proportion based on the rate of reading.
Answer
135 minutes
Answer for screen readers
The time it will take Mike to read 30 pages is 135 minutes.
Steps to Solve
- Determine the rate of reading First, we need to find out how many pages Mike reads in one minute by setting up a rate. He reads 4 pages in 18 minutes. We can calculate his rate using the formula:
$$ \text{Rate} = \frac{\text{Pages}}{\text{Time}} = \frac{4 \text{ pages}}{18 \text{ minutes}} $$
- Simplify the rate Now we simplify the rate:
$$ \frac{4}{18} = \frac{2}{9} $$
This tells us that Mike reads $\frac{2}{9}$ pages per minute.
- Calculate time to read 30 pages To find out how long it will take him to read 30 pages, we use the formula:
$$ \text{Time} = \frac{\text{Total Pages}}{\text{Rate}} $$
Substituting the values:
$$ \text{Time} = \frac{30 \text{ pages}}{\frac{2}{9} \text{ pages per minute}} $$
- Simplify the equation To divide by a fraction, we multiply by its reciprocal:
$$ \text{Time} = 30 \times \frac{9}{2} $$
- Calculate the final time Now, we just do the multiplication:
$$ \text{Time} = 30 \times 4.5 = 135 \text{ minutes} $$
So, it will take him 135 minutes to read 30 pages.
The time it will take Mike to read 30 pages is 135 minutes.
More Information
Mike reads at a rate of $\frac{2}{9}$ pages per minute, which is equivalent to about 0.22 pages per minute. Therefore, he takes a total of 135 minutes to read 30 pages.
Tips
- Confusing the rate of reading with the total time. Remember that the rate must be correctly simplified before applying it in calculations.
- Miscalculating the multiplication when converting time from pages to minutes. Always double-check your math!
