Dirk and his friends set out to sea on their annual fishing trip. There is a proportional relationship between the time (in hours) Dirk and his friends spend sailing, x, and their distance from shore (in miles), y. Write an equation for the relationship between x and y. Simplify any fractions. y = kx

To solve this problem, we are looking at a proportional relationship between the time spent sailing, x , and the distance traveled from shore, y . A proportional relationship means that as one variable changes, the other changes at a constant rate. This can be written as:
y = k x
Where y represents the distance from shore in miles, x represents the time spent sailing in hours, and k is the constant of proportionality, which is the rate of travel in miles per hour.
This equation implies that for every hour spent sailing, Dirk and his friends travel k miles.
To write the complete equation, you would need a given value for k , which represents how far Dirk and his friends sail in one hour. If more information were provided, such as y miles traveled in x hours, you could calculate k using the formula k = x y ​ .
In practical terms: If the boat travels 30 miles in 5 hours, then:
k = 5 30 ​ = 6
Therefore, the relationship would be:
y = 6 x
This shows that for every additional hour sailing, they travel 6 miles farther from shore.

Answered by danjohnbrain | 2025-07-22

The relationship between the time spent sailing ( x ) and distance from shore ( y ) is expressed by the equation y = k x , where k is the constant speed in miles per hour. For example, if Dirk and his friends travel 30 miles in 5 hours, then k = 6 , resulting in the equation y = 6 x . This means they travel 6 miles for every hour spent sailing.
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Answered by danjohnbrain | 2025-08-20