Final answer:
To find the length of the race Tess ran, a proportion can be set up with the distance she ran (3/4 mile) over the fraction of the race completed (1/3), which equals the total race length x over 1. The total race length x is found to be 2.25 miles, which is not listed in the choices given, indicating a possible error in the question or options.
Step-by-step explanation:
If Tess has run 3/4 of a mile and that distance represents only 1/3 of the entire race, then we can set up a proportion to find the total length of the race. We will set 3/4 mile over 1/3 and set that equal to x miles (the total distance of the race) over 1 (since x represents the whole race).
(3/4 mile) / (1/3) = (x miles) / 1
To solve for x, we can multiply both sides by the reciprocal of 1/3 which is 3:
3 × (3/4 mile) = x
(9/4 mile) = x
Now we simplify 9/4, which equals 2.25 miles. However, among the choices provided, there is no option for 2.25 miles. Therefore, it appears there is a mistake in the question or the options provided. Based on the information given, the total length of the race would be 2.25 miles.