For their dance unit, Yelena, Jackson, and Todd had to come up with a \(30\) second dance routine. All three of them are tap dancers, so they decided that each of them would do a \(5\) second solo tap, and the remaining \(15\) seconds would be a group tap.
During Yelena’s solo tap section, she tapped at a rate of \(5\) taps per second.
During Jackson’s solo tap section, he tapped at a rate of \(4\) taps per second.
During Todd’s solo tap section, he tapped at a rate of \(3\) taps per second.
For their group tap section, they all tapped at the slowest rate so that they could all keep up.
How many taps did each dancer do in total during the full routine?
We use a table to keep track of how many taps each dancer did during their solo.
| Dancer | Total Taps after \(1\) s | Total Taps after \(2\) s | Total Taps after \(3\) s | Total Taps after \(4\) s | Total Taps after \(5\) s |
|---|---|---|---|---|---|
| Yelena | \(5\) | \(10\) | \(15\) | \(20\) | \(25\) |
| Jackson | \(4\) | \(8\) | \(12\) | \(16\) | \(20\) |
| Todd | \(3\) | \(6\) | \(9\) | \(12\) | \(15\) |
Since they all tapped at the slowest rate for the group tap, then they all tapped at \(3\) taps per second, which is the same as Todd’s rate in the solo. From the table above, we know that in \(5\) seconds, Todd tapped \(15\) times. Then at this rate, in \(10\) seconds they would tap \(30\) times, and in \(15\) seconds they would tap \(45\) times.
Then we can conclude the following:
Yelena tapped a total of \(25 + 45 = 70\) times during the full routine.
Jackson tapped a total of \(20 + 45 = 65\) times during the full routine.
Todd tapped a total of \(15 + 45 = 60\) times during the full routine.