Math Problem Statement

Raul biked at a steady speed during his 8-mile ride. He finished the ride in 4/5 hour. What is Raul’s speed in miles per hour?

Solution

The problem asks to find Raul's speed in miles per hour, given that he biked 8 miles in 45\frac{4}{5} of an hour.

The formula for speed is:

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

In this case, the distance is 8 miles, and the time is 45\frac{4}{5} of an hour. The unit rate is found by dividing the distance by the time:

Speed=845=8×54=8×54=404=10miles per hour.\text{Speed} = \frac{8}{\frac{4}{5}} = 8 \times \frac{5}{4} = \frac{8 \times 5}{4} = \frac{40}{4} = 10 \, \text{miles per hour}.

Thus, Raul's speed is 10 miles per hour.

Would you like more details on how this was calculated or have any questions?

Here are 5 related questions to expand your understanding:

  1. If Raul biked 12 miles in 34\frac{3}{4} hour, what would his speed be?
  2. How would the speed change if the time increased to 1 hour but the distance stayed the same?
  3. What is the meaning of a unit rate in the context of this problem?
  4. Can the unit rate ever be a decimal, and how would you convert it from a fraction?
  5. How would Raul's speed be affected if the distance were halved but the time remained the same?

Tip: When dividing by a fraction, multiply by its reciprocal to simplify the calculation.

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Math Problem Analysis

Mathematical Concepts

Ratios
Fractions
Unit Rate

Formulas

Speed = Distance / Time

Theorems

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Suitable Grade Level

Grade 6-7