Question

Lisa is running the Challenge of Champions obstacle race at her summer camp. She runs
3
4
of a mile, but then she twists her ankle while going up the Mounds of Doom. Lisa still has
1
2
of a mile left to run, so she drops out of the race.
Which equation can you use to find the total distance d of the race?
Solve this equation for d to find the total distance of the race.
To write a fraction, use a slash ( / ) to separate the numerator and denominator.
miles

Answer 1

To find the total distance \( d \) of the race, we can express the distance Lisa ran and the distance she has left to run in terms of \( d \).

Lisa ran \( \frac{3}{4} \) of a mile and has \( \frac{1}{2} \) of a mile left to run. Together, these distances equal the total distance \( d \):

\[
\frac{3}{4} + \frac{1}{2} = d
\]

Next, we need to solve for \( d \). First, we express \( \frac{1}{2} \) with a common denominator of 4:

\[
\frac{1}{2} = \frac{2}{4}
\]

Now we can substitute this back into the equation:

\[
\frac{3}{4} + \frac{2}{4} = d
\]

Now, we can add the two fractions:

\[
\frac{3 + 2}{4} = d
\]

\[
\frac{5}{4} = d
\]

Thus, the total distance \( d \) of the race is:

\[
d = \frac{5}{4} \text{ miles}
\]

In decimal form, this is 1.25 miles. Therefore, the total distance of the race is:

\[
\frac{5}{4} \text{ miles}
\] or 1.25 miles.