To determine the meter mark where Ario will be when Miguel starts the race, let's follow the steps below:
1. Identify Given Constants:
- Miguel and Ario are both initially standing 3 meters from one side of a 25-meter pool.
[tex]\( x_1 = 3 \)[/tex] meters.
- The other side of the pool is at [tex]\( x_2 = 25 \)[/tex] meters.
[tex]\( x_2 = 25 \)[/tex] meters.
- We are given the ratio of Ario's completed meters to remaining meters as [tex]\( 1:4 \)[/tex]. Thus, [tex]\( m = 1 \)[/tex] and [tex]\( n = 4 \)[/tex].
2. Determine the Distance from Their Starting Point to the Opposite End:
- This distance is [tex]\( x_2 - x_1 \)[/tex].
[tex]\[
x_2 - x_1 = 25 - 3 = 22 \text{ meters}
\][/tex]
3. Calculate the Proportion of the Total Distance Ario Will Have Completed:
- We use the ratio [tex]\( \frac{m}{m+n} \)[/tex] to find this proportion. Since [tex]\( m = 1 \)[/tex] and [tex]\( n = 4 \)[/tex]:
[tex]\[
\frac{m}{m+n} = \frac{1}{1+4} = \frac{1}{5} = 0.2
\][/tex]
4. Find the Distance Ario Will Have Travelled from His Starting Point:
- Multiplying the proportion by the total distance from [tex]\( x_1 \)[/tex] to [tex]\( x_2 \)[/tex]:
[tex]\[
\text{Distance travelled} = 0.2 \times 22 = 4.4 \text{ meters}
\][/tex]
5. Determine Ario's Position in the Pool:
- Adding the distance Ario has traveled to his starting position at [tex]\( x_1 \)[/tex]:
[tex]\[
x = 3 + 4.4 = 7.4 \text{ meters}
\][/tex]
Therefore, Ario will be at the 7.4-meter mark when Miguel starts the race.
So, the correct answer is:
[tex]\[
7.4 \text{ meters}
\][/tex]
