A boat is navigating a river with a current speed of 2 km/h. It takes the boat 75 minutes longer to cover a distance of 56 km upstream than it does to cover 45 km downstream. Additionally, the boat travels upstream for 90 minutes and downstream for 110 minutes. Determine the total distance covered by the boat.

Solution

Let the speed of the boat in still water = 'x' km/h Then, upstream and downstream speed of the boat are (x - 2) km/h and (x + 2) km/h, respectively According to the question, {56/(x - 2)} - {45/(x + y)} = (75/60) Or, (56x + 112 - 45x + 90) ÷ (x² - 4) = 1.25 Or, 11x + 202 = 1.25x² - 5 Or, 1.25x² - 11x - 207 = 0 Or, 5x² - 44x - 828 = 0 Or, 5x² - 90x + 46x - 828 = 0 Or, 5x(x - 18) + 46(x - 18) = 0 Or, (5x + 46)(x - 18) = 0 So, x = 18 (since speed cannot be negative). Therefore, upstream and downstream speed of the boat is 16 km/h and 20 km/h Total distance travelled = 16 X (90/60) + 20 X (110/60) = 24 + (110/3) = (182/3) km