Answer:
The rate of wind is 9 miles per hour.
Step-by-step explanation:
We are given the following information:
A boater travels 27 miles per hour on the water on a still day.
[tex]\text{Speed} = \displaystyle\frac{\text{Distance}}{\text{Time}}\\\\\text{Time} = \displaystyle\frac{\text{Distance}}{\text{Speed}}[/tex]
The w be the rate of wind.
27 + w = speed with the wind
27 - w = speed against the wind
Time taken by him to travel with the wind =
[tex]\displaystyle\frac{42}{27+w}[/tex]
Time taken by him to travel against the wind =
[tex]\displaystyle\frac{21}{27-w}[/tex]
Since, the time is equal,
[tex]\displaystyle\frac{42}{27+w} = \displaystyle\frac{21}{27-w}\\\\42(27-w) = 21(27+w)\\1134 - 42w = 567 + 21w\\63w = 567\\\\w = \frac{567}{63} = 9[/tex]
Thus, the rate of wind is 9 miles per hour.
