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A motor boat whose speed is …

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A motor boat whose speed is 20km/hr in still water takes 1hr more to go 21km upstream than return downstream to the same spot. Find the speed of the stream.

Posted by Jaleela Siddique 8 years ago

CBSE > Class 10 > Mathematics

1 answers

Rajeev Malhotra 8 years ago

Speed of boat = 20 km/h and Speed of stream = x km/h

Speed of boat downstream = (20+x ) km/h

Speed of boat upstream = (20-x) km/h

Distance = 21 km

Time taken by boat to go upstream t₁ = 21/(20 -x)

Time taken by boat to go downstream = 21/(20+x)

It is given that 21/(20-x) - 21/(20+x) = 1

21(20+x)- 21(20-x)/(20-x)(20+x) = 1

420+21x -420+21x/400-x² = 1

42x/ 400-x² = 1

42x = 400-x²

x² +42x - 400=0

x²+50x-8x-400=0

x(x+50)-8(x+50)=0

(x-8)(x+50)= 0

x= 8 or x=-50

x= 8 km/h because speed can not be negative.

2Thank You

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