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

  1. 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:

$$ \text{Rate} = \frac{\text{Pages}}{\text{Time}} = \frac{4 \text{ pages}}{18 \text{ minutes}} $$

  1. 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.

  1. 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:

$$ \text{Time} = \frac{30 \text{ pages}}{\frac{2}{9} \text{ pages per minute}} $$

  1. Simplify the equation To divide by a fraction, we multiply by its reciprocal:

$$ \text{Time} = 30 \times \frac{9}{2} $$

  1. 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!
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