A boat 27 m long floats in still water. A dog floats along the boat at a speed of 5 km / h.

| August 11, 2021 | education

A boat 27 m long floats in still water. A dog floats along the boat at a speed of 5 km / h. From bow to stern and back, he swims in 1.8 minutes. What is the speed of the boat?

When the dog swims from bow to stern, that is, against the movement of the boat, its speed is added to the speed of the boat. When a dog swims from stern to bow, that is, in the direction of the boat, its speed relative to the boat is equal to the difference between its speed and the speed of the boat. Let’s translate the speed of the dog in m / min: 5 km / h * 1000/60 = 83.33 m / min.
S = 27 m; ttot = 1.8 min; Vp = 83.33 m / min; Vк is the speed of the boat.
S / (Vp-Vk) + S / (Vp + Vk) = ttotal; we bring fractions to a common denominator (Vp + Vk) (Vp-Vk): (S (Vp + Vk) + S (Vp-Vk)) / (Vp + Vk) (Vp-Vk) = ttotal; multiply both parts by (Vp + Vk) (Vp-Vk): S (Vp + Vk) + S (Vp-Vk) = ttotal * (Vp + Vk) (Vp-Vk); we open the brackets and simplify: Vk ^ 2 = (ttot * Vp ^ 2-2 * S * Vp) / ttot; we substitute the known data, calculate the square root, we get Vk = 66.66 m / min.
Answer: 66.66 m / min



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