Math Problem Statement

Brian is riding his bike. He biked a distance of 14 miles at a rate of 14 miles per hour. Rearrange the distance formula, d = rt, to solve for Brian's time in minutes. (1 hour = 60 minutes)

Solution

We are given the distance formula:

d=rtd = rt

Where:

  • dd is the distance,
  • rr is the rate or speed,
  • tt is the time.

To solve for time (tt), we can rearrange the formula as follows:

t=drt = \frac{d}{r}

Now, let's substitute the known values. Brian biked 14 miles (d=14d = 14) at a rate of 14 miles per hour (r=14r = 14):

t=1414=1 hourt = \frac{14}{14} = 1 \text{ hour}

Since we want the time in minutes, and 1 hour is equal to 60 minutes:

t=60 minutest = 60 \text{ minutes}

Therefore, Brian's biking time is 60 minutes.

Would you like more details or have any questions?

Here are 5 related questions:

  1. If Brian biked at a speed of 10 miles per hour, how long would it take him to cover 14 miles?
  2. How would the time change if the distance were doubled but the speed stayed the same?
  3. What is the formula to convert hours to minutes in such problems?
  4. If Brian biked for 45 minutes at the same rate, how far would he travel?
  5. How would you use the distance formula for a journey with varying speeds?

Tip: Always check the units in problems like these to ensure the result is in the desired form (hours, minutes, etc.).

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Math Problem Analysis

Mathematical Concepts

Algebra
Distance-Rate-Time Problems
Unit Conversion

Formulas

d = rt
t = d/r

Theorems

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Suitable Grade Level

Grades 6-8