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Teja Varma

· started a discussion

· 1 Months ago

option method (Question: 123648.0 )

how to go through option method for this question

Question:
A boat travels upstream from Q to P and downstream from P to Q in 3 hours. If the distance between P to Q is 4 km and the speed of the stream is 1 km/hr, then what is the speed of the boat in still water?
Options:
A) 4.5 km/hr 
B) 5.2 km/hr 
C) 2.5 km/hr
D) 3 km/hr
E) None of these
Solution:

Ans: (d) Let the speed of the boat in still

water be x km. /hr. 

\(\therefore \)The speed of the boat along the stream = (x+ 1) km./hr. and the speed of the boat against the stream = (x - 1) km/hr.

\(\therefore \cfrac{4}{x+1}+\cfrac{4}{x-1}\)  = 3 hours

(because time = \(\cfrac{Dist}{Speed}\)


\(\cfrac{4(x+1+x-1)}{(x+1)(x-1)}\ =3\)

or, 3x2 - 8x - 3=0

or, 3x2 - 9x + x - 3 = 0

or, (x - 3)(3x + 1) = 0

\(\therefore\) x = 3 or, \(-\cfrac{1}{3}\)  (Speed cannot be in -ve)

Hence, the speed of the boat in still water is 3 km./hr.

kanhaiya jha

· commented

· 1 Months ago

:)

Teja Varma

· commented

· 1 Months ago

THANQ

Pankaj Singh

· commented

· 1 Months ago

put option as x you you will get answer
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