Question

A boater travels 33 miles per hour on the water on a still day. During one particular windy day, he finds that he travels 28 miles with the wind behind him in the same amount of time that he travels 14 miles into the wind. Find the rate of the wind.

Answer 1

The rate of the wind is 3 miles per hour, calculated by setting up equations for the boater's speed with and against the wind and solving for the wind speed.

Step-by-step explanation:

When a boater travels with the wind, his effective speed is the sum of his speed in still water and the wind speed. Conversely, when traveling into the wind, his effective speed is his speed in still water minus the wind speed. Let's denote the wind speed as w. Hence, with the wind, the boater's speed would be 33 + w and against the wind, the speed would be 33 - w. Given that the boater travels 28 miles with the wind and 14 miles against the wind in the same amount of time (t), we can write two equations:

With the wind: 28 = (33 + w) × t

Against the wind: 14 = (33 - w) × t

Dividing the second equation by the first one gives us:

14 / 28 = (33 - w) / (33 + w)

This simplifies to:

1 / 2 = (33 - w) / (33 + w)

By cross-multiplying and solving for w, we find that:

w = 3 mph.

Therefore, the rate of the wind is 3 miles per hour.

Answer 2

W = speed of wind (33 + W = speed with) (33-W = speed against) 28/(33+w)=14/(33-w), cross multiply 14/(33+w)=28/(33-w), 462+14w=924-28w, 42w=462, w=11