A boat travels upstream from Point A to Point B in 5 hours. The same boat travelling the same distance in still water takes 50 minutes more than the time taken to travel downstream. Then what is the time taken to travel downstream from Point A to Point B (Given that it is more than 2 hours)?
Answers
Given : A boat travels upstream from Point A to Point B in 5 hours. The same boat travelling the same distance in still water takes 50 minutes more than the time taken to travel downstream.
To find : time taken to travel downstream from Point A to Point B
Solution:
Let say Boat Speed = B km/hr
Stream Speed = S km/hr
Upstream Speed = B - S km/hr
Time = 5 hrs
Distance = Speed * time = (B - S) * 5 km
Time taken in still water = D/B hr = (B - S) * 5 / B hr
Time taken in Down stream Speed = D/(B + S) = (B - S)*5/ ( B + S) hr
(B - S) * 5 / B = (B - S)*5/ ( B + S) + 50/60
=> (B - S) / B = (B - S)/ ( B + S) + 1/6
=> (B - S) / B - (B - S)/ ( B + S) = 1/6
=> (B - S) ( 1 /B - 1/(B + S) ) = 1/6
=> (B - S) ( B + S - B ) = B (B + S) /6
=> (B - S) S = B ( B + S) /6
=> 6BS - 6S² = B² + BS
=> B² - 5BS + 6S² = 0
=> B² - 2BS - 3BS + 6S² = 0
=> B ( B - 2S) - 3S(B - 2S) = 0
=> ( B - 3S) (B - 2S) = 0
=> B = 3S or B = 2S
Time taken in Down stream Speed = (B - S)*5/ ( B + S) hr
B = 3S
= ( 3S - S) * 5 / (3S + S) = 10S/4S = 2.5 hrs
B = 2S
= (2S - S) * 5 / (2S + S) = 5S/3S = 1.33 hrs
Given that it is more than 2 hours
Hence 2.5 hrs is correct Answer
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