# a boat travels at 15km/hr in still water. in travelling 45km downstream from town A to town B it completes the journey in 75 minutes less then it takes for the return journey. at what stream does the river flow?

Let the speed of river be x km/hr down stream. Time = Distance / speed Since river flows downstream, speed of boat down stream = Speed of boat + speed of river = (15 + x). Since river flows downstream, speed of boat upstream = Speed of boat - speed of river = (15 - x). Time Upstream - Time Downstream = 75 minutes Time Upstream = 45 / (15 - x) Time Downstream = 45 / (15 + x) 75 minutes = 75/60 = 5/4 hours Time Upstream - Time Downstream = 75 minutes = 5/4 hours 45 / (15 - x) - 45 / (15 + x) = 5/4 Divide both sides by 45 1 / (15 - x) - 1 / (15 + x) = (5/4)*(1/45) 1 / (15 - x) - 1 / (15 + x) = 1/36 ((15 + x) - (15 -x)) / (15-x)(15+x) = 1/36 (15 +x - 15 +x) / (15-x)(15+x) = 1/36 2x / (15-x)(15+x) = 1/36 (15-x)(15+x) = 2x*36 (15-x)(15+x) = 72x 225 - x² = 72x 0 = x² + 72x -225 x² + 72x -225 = 0 This is a quadratic function, use a calculator that can solve the function, by inputting the function. x = 3, or -75. Since we are solving for speed, we can not have negative values. x = 3 is the only valid solution. Speed of the river = 3 km/hr downstream.