There is a boat going from point A to B. It is 180 km from A to B. From point A to B is going downstream, so it only takes 10 hours. To get from point B to A, is upstream so it takes 15 hours. It rains so the river moves faster, and point A to B only takes 9 hours now. Now, how long will it take to get from point B to point A? Can you please help me with this? Explain how to do this problem.
Let b denote the speed of the boat and let c denote the speed of the current. Express the following quantities through b and c.
(1) The speed of the boat downstream without rain.
(2) Time it takes for the boat to go from A to B without a rain (use the result from (1)).
(3) The speed of the boat upstream without rain.
(4) Time it takes for the boat to go from B to A without a rain (use the result from (3)).
Equate the result from (2) to 10 and the result from (4) to 15. You'll get a system of two equations in variables b and c. Solve it to find b and c.
Now, let r denote the increase of the speed of the current due to the rain. Use the values of b and c to express the current speed and the boat speed downstream during rain through r, find the time it takes to go from A to B during rain and equate it to 9. This gives you an equation in r, from which you can find r. Finally, find the boat speed upstream during rain and answer the main question.
Edit: Moved things around slightly.
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