Question 1109352
Henry's speed is {{{400m/"2.5 minutes"=160}}}{{{m/minute}}} .
Harriet's speed is {{{400m/"2 minutes"=200}}}{{{m/minute}}} .
in {{{x}}} minutes Henry will have run {{{160x}}} meters,
and Harriet will have run {{{200x}}} meters.
When Harriet laps Henry,
she will have run {{{400m}}} (one full lap) longer than Henry.
That translates as
{{{200x=160x+400}}} .
Solving that equation:
{{{200x=160x+400}}}
{{{200x-160x=400}}}
{{{40x=400}}}
{{{x=400/40}}}
{{{x=10}}} .
It seems to be that Harriet will lap Henry after {{{highlight(10 minutes)}}} .
Let's verify.
In 10 minutes Harry will have run {{{4laps=10minutes/"2.5 minutes"}}} ,
and Harrriet will have run {{{5laps=10minutes/"2 minutes"}}} .
 
NOTE: We did not need to know the size of the track, because we could have measure their speeds in laps per minute instead of meters per minute.
For this particular problems, we could also have figured out the answer by listing how long it took for Henry and for Harriet to run 1, 2, 3, 4, 5, ... laps.
For Henry:
{{{matrix(2,7,laps,1,2,3,4,5,"...",
minutes,2.5,5,7.5,10,12.5,"...")}}} .
For Harriet:
{{{matrix(2,7,laps,1,2,3,4,5,"...",
minutes,2,4,6,8,10,"...")}}} .
It would not have been so easy, if Harriet had lapped Henry after 4.3 laps for Henry and 5.3 laps for Harriet.