Mathematics: Aboater travels 27 miles per hour on the water on a still day. during one particularly windy day, he finds that he travels 42 miles with the wind behind him in the same amount of time that he travels 21 miles into the wind. find the rate of the wind.

Aboater travels 27 miles per hour on the water

Ответ:

jakester00792

10.01.2022

Mathematics

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.

$\text{Speed} = \displaystyle\frac{\text{Distance}}{\text{Time}}\\\\\text{Time} = \displaystyle\frac{\text{Distance}}{\text{Speed}}$

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 =

$\displaystyle\frac{42}{27+w}$

Time taken by him to travel against the wind =

$\displaystyle\frac{21}{27-w}$

Since, the time is equal,

$\displaystyle\frac{42}{27+w} = \displaystyle\frac{21}{27-w}\\\\42(27-w) = 21(27+w)\\1134 - 42w = 567 + 21w\\63w = 567\\\\w = \frac{567}{63} = 9$

Thus, the rate of wind is 9 miles per hour.

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Ответ:

BobJRJR

20.06.2020

Mathematics

sides are proportional and angles are congruent

Step-by-step explanation:

Every segment in ABCDEFG is parallel to, and double the length of, the corresponding segment in HIJKLMN. All corresponding angles are congruent. Thus, the definition of similar polygons is met:

corresponding sides are angles are congruent.

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Aboater travels 27 miles per hour on the water on a still day. during one particularly windy day, he finds that he travels 42 miles with the wind behind him in the same amount of time that he travels 21 miles into the wind. find the rate of the wind.

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