Question

Mateo is running the Challenge of Champions obstacle race at his summer camp. He runs
3

4
of a mile, but then he twists his ankle while going up the Mounds of Doom. Mateo still has
1

2
of a mile left to run, so he 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.

Answer 1

To find the total distance \( d \) of the race, we know two key pieces of information:

1. Mateo has run \( \frac{3}{4} \) of a mile.
2. He has \( \frac{1}{2} \) of a mile left to run.

Since these two segments of his run make up the entire distance of the race, we can express this relationship with the following equation:

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

To solve for \( d \), we need to find a common denominator for the fractions \( \frac{3}{4} \) and \( \frac{1}{2} \). The least common denominator (LCD) of 4 and 2 is 4.

Now we can rewrite \( \frac{1}{2} \) using this common denominator:

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

Now substitute this back into the equation:

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

Now, we can add the fractions:

\[
d = \frac{3 + 2}{4} = \frac{5}{4}
\]

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

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

In decimal form, this is:

\[
d = 1.25 \text{ miles}
\]

So the total distance of the race is \( \frac{5}{4} \) miles or 1.25 miles.