A motor boat, whose speed is 24 km/hr in still water, takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream?

  8 km/h

Step-by-step explanation:

Let x represent the speed of the stream in km/h. The relation between time, sped, and distance is ...

  time = distance/speed

Upstream, the speed of the current is subtracted from the speed of the boat in still water to obtain the speed of progress relative to the bank. Downstream, the current speed adds to the boat speed. The difference in travel times in hours can be written as ...

  32/(24-x) -32/(24+x) = 1

Multiplying by the product of denominators, we have ...

  32(24+x) -32(24-x) = (24+x)(24-x)

  64x = 24^2 -x^2

  x^2 +64x +32^2 = 24^2 +32^2 . . . . . add x^2 and complete the square

  (x +32)^2 = 40^2 . . . . . . . . write as squares

  x = -32 +40 . . . . . . . . . . . . . take the positive square root

  x = 8

The speed of the current is 8 km/h.

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I find a graphing calculator to be a quick and easy way to solve problems like this.

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hope this ! have a great day.

-wfz