commonly used formula 

Distance Formula Overview

• The distance formula in mathematics is a fundamental equation used to calculate the distance traveled by an object.

  • Formula:

  • The most frequently used formula is represented as follows:

    • $d = r \times t$

  • Where:

    • $d$ = distance

    • $r$ = rate (speed)

    • $t$ = time

• The formula can also be rearranged to solve for rate or time:

  • Rate Formula:

  • $r = \frac{d}{t}$

  • Time Formula:

  • $t = \frac{d}{r}$

Example Application of the Distance Formula

Problem Statement

• Given:

  • Sarah drives at a rate of 45 miles per hour for a total of 4 hours.

• Goal: Calculate how far Sarah drives.

Variables Defined

• Let:

  • $D$ = distance (unknown)

  • $R$ = rate = 45 miles per hour

  • $T$ = time = 4 hours

Steps to Solve

1. Substitute the known values into the distance formula:

   • $D = R \times T$

   • Replacing with known values:

   • $D = 45 \text{ miles/hour} \times 4 \text{ hours}$

2. Calculate the distance:

   • Multiply the rate by time:

   • $D = 180 \text{ miles}$

Conclusion

• Therefore, Sarah would drive a total of 180 miles over the given time at the specified rate.

  • Answer:

  • Sarah drives 180 miles.