Math Problem Statement

Every time Joe runs, he runs 2/4 of a mile whenever Jane runs. She wants four over four of a mile if Joe runs two times a week how many times Jane run to cover the same distance as Joe.

Solution

Let's break down the problem into parts.

  1. Joe's running distance:
    Every time Joe runs, he runs 24=12\frac{2}{4} = \frac{1}{2} mile.

  2. Jane's running distance:
    Jane runs 44=1\frac{4}{4} = 1 mile each time she runs.

  3. Joe's weekly running:
    Joe runs twice a week, covering 2×12=12 \times \frac{1}{2} = 1 mile in a week.

  4. How often Jane needs to run to match Joe's weekly distance:
    Since Jane runs 1 mile each time, she only needs to run once per week to cover the same distance that Joe runs in a week.

Final Answer

Jane would need to run 1 time per week to cover the same distance as Joe when he runs twice a week.

Would you like a deeper explanation, or do you have any questions?

Here are some related questions for further practice:

  1. If Joe increased his weekly runs to 4, how many times would Jane need to run?
  2. What if Jane wanted to run only half the distance Joe runs; how often should she run?
  3. If Jane’s running distance changed to 3/4 of a mile, how many times would she need to run?
  4. How many miles would Joe run in a month (4 weeks) at his current pace?
  5. If Joe and Jane both wanted to cover 5 miles in a week, how often should each run?

Tip: For unit comparisons, break down the problem into smaller steps to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Fractions
Distance
Proportions

Formulas

Distance = Rate × Time
Proportional Relationships

Theorems

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Suitable Grade Level

Grades 4-6