Question

Lin runs $5$ laps around a track in $6$ minutes. If Lin runs $21$ laps at the same rate, how long will it take her?

Answer 1

Determine the time taken by Lin to run $\mathbf{21}\mathbf{}$laps using the Unitary Method.

The time taken varies in direct proportion with the number of laps.

The time taken by Lin to run $5$ laps is $6$ minutes. So, the time taken by Lin to run $1$ lap is $\frac{6}{5}$ minutes.

Thus, the time taken by Lin to run $21$ laps is $\frac{6}{5}\times 21$ minutes.

Evaluate the expression:
$\begin{array}{rcl}\text{Time take to run}21\text{laps}& =& \frac{6}{5}\times 21\text{minutes}\\ & =& \frac{126}{5}\text{minutes}\\ & =& \left(25+\frac{1}{5}\right)\text{minutes}\\ & =& 25\text{minutes}+\frac{1}{5}\text{minutes}\\ & =& 25\text{minutes}+\frac{1}{5}\times 60\text{seconds}\\ & =& 25\text{minutes}+12\text{seconds}\\ & =& 25\text{minutes and}12\text{seconds}\end{array}$

Thus, it will take Lin $\mathbf{25}\mathbf{}\mathbf{\text{minutes and}}\mathbf{}\mathbf{12}\mathbf{}\mathbf{\text{seconds}}$ to run $\mathbf{21}\mathbf{}$laps at the same rate.