A rectangularreservoirhas a 1km difference betweenitssides. Two fisherrhen simultaneously leave one vertex of therectangle for a point located at the opposite vertex. Onefisherman crosses the reservoir in a-boat, the other walks alongthe bank. Find the size of the reservoir if each ofthem has aspeed of 4 km/hr and one of them arrives half an hour earlierthan the other
Question
A rectangularreservoirhas a 1km difference betweenitssides. Two fisherrhen simultaneously leave one vertex of therectangle for a point located at the opposite vertex. Onefisherman crosses the reservoir in a-boat, the other walks alongthe bank. Find the size of the reservoir if each ofthem has aspeed of 4 km/hr and one of them arrives half an hour earlierthan the other
Solution
Let's denote the sides of the rectangle as a and b, where a > b. The difference between the sides is 1 km, so a = b + 1 km.
The fisherman who crosses the reservoir in a boat travels a distance of √(a² + b²) km. Since his speed is 4 km/hr, the time he takes is √(a² + b²) / 4 hours.
The fisherman who walks along the bank travels a distance of a + b km. His time is (a + b) / 4 hours.
According to the problem, the fisherman who walks along the bank arrives half an hour later than the one who crosses the reservoir in a boat. Therefore, we can write the equation:
√(a² + b²) / 4 = (a + b) / 4 - 0.5
Solving this equation, we get a = 3 km and b = 2 km. Therefore, the sides of the reservoir are 3 km and 2 km.
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