Question 838243
The requirement refers to a table that is the way the teacher would solve the problem. Not being in your class, I do not know the teacher's way to solve it.
 
MY WAY:
Tom runs 1 lap in {{{40}}} seconds, so Tom's speed, in laps per second, is {{{1/40}}} .
Tom and Tyanna together cover 1 lap in {{{15}}} seconds, so their speeds add up to {{{1/15}}} laps per second.
Tyanna's speed, in laps per second, is
{{{1/15-1/40=8/120-3/120=5/120=1/24}}} .
That means that Tyanna runs 1 lap in {{{24}}} seconds.
It took {{{12*24seconds=288seconds}}} for Tyanna to run her 12 laps.
During that time Tyanna and Tom passed each other {{{highlight(19 times)}}} because
{{{288seconds/"15 seconds"=19.2}}}
They passes each other for the 19th time
{{{19*15seconds=285seconds}}} after they started running, and 3 seconds later Tyanna was finished.
To ruAt {{{40}}} seconds per lap, it would take Tom a total of
{{{12*40seconds=480seconds}}} to run 12 laps, the same distance that Tyanna ran.
Since Tyanna finished in {{{288seconds}}} , Tom will need to run
{{{480seconds-288seconds=192seconds}}} more after Tyanna is finished.
That is {{{highlight(3minutes+12seconds)}}} , because dividing {{{192seconds}}} by {{{60}}} seconds per minute gives you a quotient of 3 minutes and a remainder of 12 seconds.
During those extra {{{192seconds}}} , at a speed of {{{1/40}}} laps per second Tom will cover
{{{192*(1/40)}}}={{{highlight(4.8laps)}}}