Mathematics
heruelbarca
5

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?

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(1) Answers
Llama11

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.

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