Question

A boat leaves a dock at 1:00 pm and travels due south at a speed of 20 km/h. Another boat has been heading due east at 15 km/h and reaches the same dock at 2:00 pm. How many minutes after 1:00 pm were the two boats closest together? (round your answer to the nearest minute. ).

Answer 1

To find the point at which the two boats are closest together, we can use the Pythagorean theorem and take the derivative of the distance function.

Step-by-step explanation:

To find the point at which the two boats are closest together, we need to calculate the distance between them at different times. Let's assume that t hours have passed since 1:00 pm. The boat traveling south will have traveled a distance of 20t km, and the boat traveling east will have traveled a distance of 15 km. We can use the Pythagorean theorem to find the distance between the two boats:

d = sqrt((20t)^2 + 15^2)

Next, we can take the derivative of the distance function with respect to t and set it equal to zero to find the minimum distance:

d' = 0

Solving this equation will give us the value of t when the two boats are closest together.