A motor-boat whose speed is 4 km/h in still water , take 2 hours more to row 6 km upstream than to return downstream. Find the speed of the stream.
please guide me.
Answers
Answer:
2 km/h is the speed of Stream
Step-by-step explanation:
The speed of motorboat= 4 kmph
Let speed of stream be x
speed of boat while going upstream= 4-x
speed of boat while going downstream=4+x
Distance is same for upstream and downstream.
Let time taken in downstream be 't', then time taken in upstream=t+2 (In hrs)
So (4-x)(t+2)=(4+x)(t)
On solving, we get- t=4-x/x
As distance = 6 Km
Distance= speed of downstream x time taken in downstream
6=(x+4)*t
Put value of t=4-x/x
ON solving, we get..
x^2+6x-16+0
x^2+8x-2x-16=0
x(x+8)-2(x+8)=0
(x+8)(x-2)
Hence, x= -8,2
As x is speed it cannot be negative, hence x= 2kmph
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Answer:
2 Km / h
Step-by-step explanation:
Speed of the motor-boat in still water = 4 Km / h
Let the speed of the stream be 'x' Km / h
Distance traveled by motor boat in upstream and downstream = 6 Km
Speed of the motor boat upstream = Speed of the motor boat - Speed of the stream = ( 4 - x ) Km/ / h
Time taken by motor boat upstream = Distance / Speed = 6 / ( 4 - x ) hours
Speed of the motor boat downstream = Speed of the motor boat + Speed of the stream = ( 4 + x ) Km / h
Time taken by motor boat downstream = Distance / Speed = 6 / ( 4 + x ) hours
Given :
Time taken by motor boat upstream = Time taken by motor boat downstream + 2 hours
⇒ 6/( 4 - x ) = 6/( 4 + x ) + 2
⇒ 6/( 4 - x ) - 6/( 4 + x ) = 2
⇒ 3/( 4 - x ) - 3/( 4 + x ) = 1
Multiplying every term with ( 4 - x )( 4 + x )
⇒ 3( 4 + x ) - 3( 4 - x ) = ( 4 - x )( 4 - x )
⇒ 12 + 3x - 12 + 3x = 4² - x²
⇒ x² + 6x - 16 = 0
⇒ x² + 8x - 2x - 16 = 0
⇒ x( x + 8 ) - 2( x + 8 ) = 0
⇒ ( x - 2 )( x + 8 ) = 0
⇒ x - 2 = 0 OR x + 8 =0
⇒ x = 2 OR x = - 8 ( not possible since speed cannot be negative )
⇒ x = 2