Question

Solve for \[r\] in \[d = rt\].

Answer 1

Hint: To solve for any variable in an equation, we isolate it to one side of the equation and the other terms to the other side of the equation.

Complete step-by-step answer:
Rewrite the equation as follows to bring the unknown term to be found to the left hand side of the equation:
\[rt = d\]
Divide each term by the coefficient of the unknown term to be found, in this case the coefficient of the unknown term \[r\] is \[t\], so divide both sides of the equation by \[t\]:
\[\dfrac{{rt}}{t} = \dfrac{d}{t}\]
Cancel the common factor of \[t\]:
\[r = \dfrac{d}{t}\]
Hence we find that \[r = \dfrac{d}{t}\].

Additional information:
The given formula \[d = rt\], is known as the distance, rate(speed) , time formula, i.e., for an object moving at an uniform rate(speed), the distance travelled in time \[t\] is given by the formula:
 \[d = rt\] [where \[d = \] distance travelled, \[t = \] time elapsed, \[r = \] rate (speed)].

Note: Whenever this formula is applied in any problem, all the quantities should be in the same system of units, like CGS , MKS, etc. The unit of \[r\] will be equal to the unit of distance, divided by the unit of time. For example if the distance is in kilometre \[\left( {km} \right)\] and time is in seconds \[(s)\], then the unit of \[r\] will be \[\dfrac{{km}}{s}\].