Answer:
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The answer is 3 km/h.
Step-by-step explanation:
The speed of the motor boat in still water is 9 km/h.
Let , the speed of the stream is x km/h.
then , the speed of the boat in downstream is ( 9 + x ) km/h and the speed of the boat in upstream is ( 9 - x ) km/h.
As , we know that ,
S = V × t ⇒ t = S/V [ Where t = time , S = displacement , V = velocity/speed]
According to the question ,
Let , the time taken in downstream is t₁ = 15/( 9 + x ) hours
And , the time taken in upstream is t₂ = 15/( 9 - x ) hours
total time taken ,
t₁ + t₂ = 3 hours 45 minutes
⇒ 15/( 9 + x ) + 15/( 9 - x ) = 3.75 hours
⇒ 15/( 9 + x ) + 15/( 9 - x ) = 15/4
⇒ 1/( 9 + x ) + 1/( 9 - x ) = 1/4
⇒ ( 9 - x + 9 + x )/( 81 - x² ) = 1/4
⇒ 18/( 81 - x² ) = 1/4
⇒ 72/( 81 - x² ) = 1
⇒ 72 = 81 - x²
⇒ x² = 9 ⇒ x = 3 km/h
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Answers & Comments
Answer:
wait I will send you the answer of this question
Answer:
The answer is 3 km/h.
Step-by-step explanation:
The speed of the motor boat in still water is 9 km/h.
Let , the speed of the stream is x km/h.
then , the speed of the boat in downstream is ( 9 + x ) km/h and the speed of the boat in upstream is ( 9 - x ) km/h.
As , we know that ,
S = V × t ⇒ t = S/V [ Where t = time , S = displacement , V = velocity/speed]
According to the question ,
Let , the time taken in downstream is t₁ = 15/( 9 + x ) hours
And , the time taken in upstream is t₂ = 15/( 9 - x ) hours
total time taken ,
t₁ + t₂ = 3 hours 45 minutes
⇒ 15/( 9 + x ) + 15/( 9 - x ) = 3.75 hours
⇒ 15/( 9 + x ) + 15/( 9 - x ) = 15/4
⇒ 1/( 9 + x ) + 1/( 9 - x ) = 1/4
⇒ ( 9 - x + 9 + x )/( 81 - x² ) = 1/4
⇒ 18/( 81 - x² ) = 1/4
⇒ 72/( 81 - x² ) = 1
⇒ 72 = 81 - x²
⇒ x² = 9 ⇒ x = 3 km/h