A boat travels 2 Km upstream in a stream flowing at 3 Km/h and, then returns downstream to the starting point in 30 minutes. The speed of the boat in still water is:
(a) 17 Km/h
(b) 9 Km/h
(c) 13 Km/h
(d) 15 Km/h
(e) None of these
Answers
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9 km/hr is your answer
Answered by
4
Answer:
The speed of the boat in still water is option b) 9 km/h
Step-by-step explanation:
Let the speed of boat in still water = x km/h
speed of stream = 3 km/h
=> speed of boat in upstream = x - 3 km/h
=> speed of boat in downstream = x + 3 km/h
Distance traveled in downstream = Distance traveled in upstream = 2 km
Total Time taken = 30 minutes = 0.5 hr
In upstream,
time = distance/speed
=> t₁ = 2/(x-3)
In downstream,
time = distance/speed
=> t₂ = 2/(x+3)
total time = 0.5
=> t₁ + t₂ = 0.5
=> 2/(x-3) + 2/(x+3) = 0.5
=> (2x + 6 + 2x - 6)/(x²-9) = 0.5
=> 4x/x²-9 = 0.5
=> x² - 9 = 8x
=> x² - 8x - 9 = 0
=> x² +x - 9x - 9 = 0
=> (x+1)(x-9) = 0
=> x = -1 or x = 9
=> x = 9 as speed can not be -ve
Hence The speed of the boat in still water is option b) 9 km/h
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