Given:
The length of the marathon is L= 46,145 yards.
The length covered by terrence is d = 23,561 yrads.
The objective is to find the remaining distance need to cover by terrence.
To calculate the remaining distance, we will use the relation,
[tex]x=L-d[/tex]On plugging the values in the above relation, we get,
[tex]\begin{gathered} x=46145-23561 \\ =22584\text{ yards} \\ \approx23000\text{ yards} \end{gathered}[/tex]Hence, Terrence needs to run about 23000 yards.