The boat sails the distance between the quays A and B in 8 minutes, and the same distance across the lake in 12 minutes.

The boat sails the distance between the quays A and B in 8 minutes, and the same distance across the lake in 12 minutes. How many minutes will it take to sail the distance between quays A and B. a) raft b) boat against the river

Let the distance between the marinas A and B be x km, then the boat’s own speed will be x: (1/5) = 5 ∙ x (km / h), and the speed of the boat along the river will be x: (2/15) = 7, 5 ∙ x (km / h), since it is known from the problem statement that the boat sails the distance between the marinas A and B in 8 minutes = 2/15 hours and the same distance across the lake swims in 12 minutes = 1/5 hour. Then the speed of the river will be 7.5 ∙ х – 5 ∙ х = 2.5 ∙ х (km / h). The raft sails the distance between marinas A and B in x: (2.5 ∙ x) = 0.4 (hours). The speed of the boat against the stream of the river will be 5 ∙ х – 2.5 ∙ х = 2.5 ∙ х (km / h). It turns out that the boat sails the distance between the marinas A and B against the river flow in x: (2.5 ∙ x) = 0.4 (hours) or in 0.4 ∙ 60 = 24 (minutes).
Answer: the raft sails the distance between the marinas A and B in 24 minutes, the boat sails the distance between the marinas A and B against the stream of the river for 24 minutes.