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A motor boat, whose speed in still water is $20$ km/h, takes $1$ hour more to go $48$ km upstream than to return downstream to the same point. Find the speed of the stream.
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(b) Let speed of stream be $x$ km/h (0.5 Mark)
Speed of boat upstream= $(20 – x)$ km/h
Speed of boat downstream = $(20 + x)$ km/h (0.5 Mark)
$\therefore \frac{48}{20-x} - \frac{48}{20+x} = 1$ (1.5 Mark)
$x^2 + 96x – 400 = 0$
$(x + 100) (x - 4) = 0$ (1 Mark)
$x = 4, x = -100$ (rejected)
Hence, speed of stream is $4$ km/h. (1.5 Mark)
(b) Let speed of stream be $x$ km/h (0.5 Mark)
Speed of boat upstream= $(20 – x)$ km/h
Speed of boat downstream = $(20 + x)$ km/h (0.5 Mark)
$\therefore \frac{48}{20-x} - \frac{48}{20+x} = 1$ (1.5 Mark)
$x^2 + 96x – 400 = 0$
$(x + 100) (x - 4) = 0$ (1 Mark)
$x = 4, x = -100$ (rejected)
Hence, speed of stream is $4$ km/h. (1.5 Mark)