Math Problem Statement

Chen bikes 2 1/2 miles in 5/12 hour. What is Chen's unit rate in miles per hour?

Solution

The problem you're working on asks to calculate the unit rate of Chen's biking speed, given that Chen bikes 2122 \frac{1}{2} miles in 512\frac{5}{12} of an hour.

To calculate the unit rate (miles per hour), follow these steps:

  1. Convert mixed fraction to improper fraction:
    212=52 miles2 \frac{1}{2} = \frac{5}{2} \text{ miles}

  2. Set up the unit rate calculation:
    The unit rate is the distance divided by the time: Unit rate=52 miles512 hours\text{Unit rate} = \frac{\frac{5}{2} \text{ miles}}{\frac{5}{12} \text{ hours}}

  3. Divide the fractions:
    Dividing by a fraction is the same as multiplying by its reciprocal: 52÷512=52×125\frac{5}{2} \div \frac{5}{12} = \frac{5}{2} \times \frac{12}{5}

  4. Simplify the expression:
    The 55's cancel out, leaving: 122=6\frac{12}{2} = 6

So, Chen's unit rate is 6 miles per hour.

The answer you entered (1.04 miles per hour) is incorrect. The correct answer is 6 miles per hour.

Do you need further details or clarifications? Here are 5 related questions to practice:

  1. How do you convert a mixed fraction into an improper fraction?
  2. How do you divide fractions in general?
  3. If Chen biked 3 miles in 34\frac{3}{4} of an hour, what would his speed be?
  4. What is the significance of unit rate in real-world problems?
  5. How can simplifying fractions help in solving rates and ratios?

Tip: When dividing by a fraction, remember to multiply by its reciprocal!

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Math Problem Analysis

Mathematical Concepts

Rates
Fractions
Division of Fractions

Formulas

Unit rate = Distance / Time
Mixed fraction conversion: a b/c = (a * c + b) / c
Dividing fractions: a/b ÷ c/d = a/b * d/c

Theorems

Reciprocal Rule: Dividing by a fraction is the same as multiplying by its reciprocal

Suitable Grade Level

Grade 6-8