A boat takes 8 hr. to cover 65 km in upstream and 75 km in downstream. While it takes 7 hr. 36 min. to cover 52 km in upstream and 90 km in downstream. Then find the speed of boat in still water.
Answer & explanation
Correct answer: option 4
Let the speed of boat = U km/h
Speed of stream = V km/hr
ATQ, \(\frac{65}{U-V}\) + \(\frac{75}{U+V}\) = 8 -------- (i)
\(\frac{52}{U-V}\) + \(\frac{90}{U+V}\) = 7\(\frac{3}{5}\) ----- (ii)
Note :- Take common factor for easy calculation
(65 , 52) (75 , 90)
⇓ ⇓ ⇓ ⇓
13 25
So, U+V = 25 and U-V = 13 satisfy the equation
Then (U) speed of boat = \(\frac{25+13}{2}\) = 19 km/hr