To determine at what meter mark Ario will be when Miguel starts the race, we can use the following formula:
[tex]\[ x = \left( \frac{m}{m + n} \right) (x_2 - x_1) + x_1 \][/tex]
where:
- [tex]\( m \)[/tex] represents the number of meters Ario has completed,
- [tex]\( n \)[/tex] represents the number of meters Ario has remaining,
- [tex]\( x_1 \)[/tex] represents Ario's starting position,
- [tex]\( x_2 \)[/tex] represents the distance to the end of the pool.
Given:
- Miguel and Ario are both standing 3 meters from one side of a 25-meter pool, so [tex]\( x_1 = 3 \)[/tex].
- The pool length is 25 meters, so [tex]\( x_2 = 25 - 3 = 22 \)[/tex] meters from their starting position.
- The ratio of Ario's completed meters to remaining meters is [tex]\( 1:4 \)[/tex], so [tex]\( m = 1 \)[/tex] and [tex]\( n = 4 \)[/tex].
Plug the values into the formula:
[tex]\[ x = \left( \frac{1}{1 + 4} \right) (22 - 3) + 3 \][/tex]
[tex]\[ x = \left( \frac{1}{5} \right) \times 19 + 3 \][/tex]
[tex]\[ x = 3.8 + 3 \][/tex]
[tex]\[ x = 6.8 \][/tex]
Hence, Ario will be at the 6.8 meter mark when Miguel starts the race. Therefore, the correct answer is 6.8 meters, rounded to the nearest tenth.
