The distance, d, an object travels is represented by the formula d = rt, where r is the rate at which the object is traveling and t is the duration of time over which the object travels. If d has units of meters and r has units of meters per minute, what must be the units of t?

A.
meters
B.
seconds
C.
meters per second
D.
minutes

1 answer

To determine the correct units for \( t \) in the equation \( d = rt \), we start with the units given in the problem.

  • The distance \( d \) is in meters (m).
  • The rate \( r \) is in meters per minute (m/min).

Now, we can rearrange the formula to solve for \( t \):

\[ t = \frac{d}{r} \]

Substituting the units we have:

\[ t = \frac{\text{meters}}{\text{meters per minute}} = \frac{m}{m/min} \]

When you divide meters by meters per minute, the meters cancel out, and you multiply by the reciprocal of the denominator:

\[ t = \frac{m \cdot \text{min}}{m} = \text{min} \]

Thus, the units of \( t \) must be minutes.

The correct answer is:

D. minutes