Math Problem Statement

Solve this question

Colton read 19 1/3 pages in 20 minutes. If he reads at a constant rate, how many pages did he read in one hour?

Solution

The problem asks how many pages Colton would read in one hour (60 minutes) given that he reads 19 1/3 pages in 20 minutes at a constant rate. Let's solve this step by step:

Step 1: Convert the mixed number

Colton reads 19 1/3 pages in 20 minutes. Convert this to an improper fraction: 1913=583 pages19 \frac{1}{3} = \frac{58}{3} \text{ pages} This is the number of pages he reads in 20 minutes.

Step 2: Determine pages per minute

Since Colton reads 583\frac{58}{3} pages in 20 minutes, the number of pages he reads per minute is: 583÷20=583×120=5860=2930 pages per minute\frac{58}{3} \div 20 = \frac{58}{3} \times \frac{1}{20} = \frac{58}{60} = \frac{29}{30} \text{ pages per minute}

Step 3: Calculate the number of pages read in 60 minutes

To find how many pages he reads in 60 minutes, multiply the pages per minute by 60: 2930×60=29×6030=174030=58 pages\frac{29}{30} \times 60 = \frac{29 \times 60}{30} = \frac{1740}{30} = 58 \text{ pages}

Final Answer:

Colton will read 58 pages in one hour (60 minutes).

Would you like further details or have any questions?

Here are five related questions:

  1. How would the result change if Colton read faster or slower?
  2. What if Colton read 25 pages in 20 minutes instead? How many in one hour?
  3. How do you convert between mixed numbers and improper fractions?
  4. How can you generalize this problem for any number of pages and minutes?
  5. What is the importance of unit rates in solving real-life problems?

Tip: Always convert mixed numbers to improper fractions before performing calculations, as it simplifies the arithmetic.

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Math Problem Analysis

Mathematical Concepts

Fractions
Rates
Unit Conversions

Formulas

Mixed number to improper fraction conversion
Rate calculation: Pages per minute = Total pages / Total time
Multiplying the rate by the total time to find the total number of pages read

Theorems

Basic rate calculation theorem (distance = rate × time analogy)

Suitable Grade Level

Grades 6-8