`(3.86)/(x)+(180.2)/(10x)+(42.2)/(5x)`
The Ironman Triathlon originated in Hawaii in 1978. The format of the Ironman has not changed since then: It consists of a 3.86-km swim, a 180.2-km bicycle ride, and a 42.2-km run, all raced in that order and without a break. Suppose an athlete bikes 10 times as fast as he swims and runs 5 times as fast as he swims. The variable x in the expression above represents the rate at which the athlete swims, and the whole expression represents the number of hours that it takes him to complete the race. If it takes him 16.2 hours to complete the race, how many kilometers did he swim in 1 hour?

Options

A. `0.85`
B. `1.01`
C. `1.17`
D. `1.87`

Answer

To solve the problem, we need to find the swimming speed \( x \) of the athlete in kilometers per hour. The total time taken to complete the Ironman Triathlon is given as 16.2 hours. The expression representing the total time is:

\[ \frac{3.86}{x} + \frac{180.2}{10x} + \frac{42.2}{5x} \]

### Step-by-Step Solution:

1. **Set up the equation**: We know that the total time taken is 16.2 hours. Therefore, we can set up the equation:
\[ 16.2 = \frac{3.86}{x} + \frac{180.2}{10x} + \frac{42.2}{5x} \]

2. **Find a common denominator**: The common denominator for the fractions is \( 10x \). We rewrite each term:
\[ \frac{3.86}{x} = \frac{3.86 \cdot 10}{10x} = \frac{38.6}{10x} \]
\[ \frac{180.2}{10x} = \frac{180.2}{10x} \]
\[ \frac{42.2}{5x} = \frac{42.2 \cdot 2}{10x} = \frac{84.4}{10x} \]

Now, substituting these back into the equation gives:
\[ 16.2 = \frac{38.6 + 180.2 + 84.4}{10x} \]

3. **Combine the numerators**: Now, we sum the numerators:
\[ 38.6 + 180.2 + 84.4 = 303.2 \]
Thus, we have:
\[ 16.2 = \frac{303.2}{10x} \]

4. **Multiply both sides by \( 10x \)**: This eliminates the fraction:
\[ 16.2 \cdot 10x = 303.2 \]
\[ 162x = 303.2 \]

5. **Solve for \( x \)**: Now, divide both sides by 162:
\[ x = \frac{303.2}{162} \]

6. **Calculate \( x \)**: Performing the division gives:
\[ x \approx 1.87 \]

### Conclusion:
The swimming speed \( x \) of the athlete is approximately \( 1.87 \) kilometers per hour.