Question

A boat travels at 15 km/hr in still water. In travelling 45 km downstream from town A to town Bit completes the journey in 75 minutes less than it takes for the return journey. At what speed does the river flow?

Answer 1

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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