Math Problem Statement

A cyclist rode 4.88 miles in 0.4 hours. How long will it take her to go 244 miles?

Solution

To determine how long it will take the cyclist to go 244 miles, we first calculate the cyclist's speed and then use it to find the time required for 244 miles.

Step 1: Calculate the speed of the cyclist.

The formula for speed is:

Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}

Substituting the given values:

Speed=4.88miles0.4hours=12.2miles per hour\text{Speed} = \frac{4.88 \, \text{miles}}{0.4 \, \text{hours}} = 12.2 \, \text{miles per hour}

Step 2: Calculate the time to travel 244 miles.

The formula for time is:

Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}

Substituting the values:

Time=244miles12.2miles per hour=20hours\text{Time} = \frac{244 \, \text{miles}}{12.2 \, \text{miles per hour}} = 20 \, \text{hours}

Final Answer:

It will take the cyclist 20 hours to travel 244 miles.


Do you have any questions or need further clarification? Here are some related questions to explore:

  1. What is the formula for converting hours to minutes?
  2. How does the speed change if the cyclist rides up a hill?
  3. What would the time be if the cyclist increased her speed to 15 mph?
  4. How is average speed calculated when multiple trips with different speeds are taken?
  5. How can you convert this calculation into a rate problem for algebra practice?

Tip: Always ensure units are consistent when performing calculations. For example, miles should match hours for speed calculations.

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Math Problem Analysis

Mathematical Concepts

Rate Problems
Distance-Time-Speed Relationship

Formulas

Speed = Distance / Time
Time = Distance / Speed

Theorems

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Suitable Grade Level

Grades 6-8