Question

a motorboat whose speed is 20 km per hour in still water takes 1 hour more to go 48 km upstream then to return downstream to the same spot find the speed of the stream

Answer 1

Heya mate,

here is your answer,

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Let the speed of stream = x km/h

Speed of boat in still water = 20 km/h

Speed in downstream = (20+x) km/h

Speed in upstream = (20−x) km/h

Time taken by boat to  cover 48 km downstream = 48/20+x hrs

Time taken by boat to cover 48 km upstream = 48/20−x hrs

Now, according to question,

48/20−x − 48/20+x = 1

$\frac{1}{20 - x} - \frac{1}{20 + x} = \frac{1}{48} \\ \\ \frac{(20 + x) - (20 - x)}{(20 - x)(20 + x)} = \frac{1}{48} \\ \\ \frac{2x}{400 - {x}^{2} } = \frac{1}{48}$

$400 - {x}^{2} = 96x \\ \\ {x}^{2} + 96x - 400 = 0$
${x}^{2} + 100x - 4x - 400 = 0$
x (x+100) - 4 (x+100) =0

(x+100) (x-4) = 0

x+100 = 0 or x-4 = 0

x = 4 or x = -100 (rejected)


So, speed of stream = 4 km/ h

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# nikzz

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Answer 2

Answer:

Step-by-step explanation: