Question 1014915
{{{x}}}= length of the acceleration phase, in meters.
{{{100-x}}}= length of the maximum speed phase, in meters.
At an average speed of {{{"2.7 m / s"}}} ,
Suki will cover the first {{{x}}} meters in
{{{x/2.7}}} seconds.
Then, she will complete the remaining {{{100-x}}}meters,
at an average speed of {{{"6.6 m / s"}}} , in
{{{(100-x)/6.6}}} seconds.
Since both stages add up to {{{18.1}}} seconds, our equation is
{{{x/2.7+(100-x)/6.6=18.1}}} .
 
Solving:
{{{x/2.7+(100-x)/6.6=18.1}}}
Multiplying both sides of the equal sign times {{{2.7*6.6}}} , we get
{{{6.6x+2.7(100-x)=18.1*2.7*6.6}}}
{{{6.6x+270-2.7x=322.452}}}
{{{6.6x-2.7x=322.452-270}}}
{{{3.9x=52.452}}}
{{{x=52.452/3.9=13.449}}}(rounded to 3 decimal places).
So, to the nearest tenth of a meter, Suki's initial acceleration phase is {{{highlight(13.4)}}} meters long.