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A boat goes 27 km upstream and 33 km downstream in 6 hours. In the same time it can go 36 km upstream and 22 km downstream. How much time will it take to go 36 km upstream and 44 km downstream?

A boat goes 27 km upstream and 33 km downstream in 6 hours. In the same time it can go 36 km upstream and 22 km downstream. How much time will it take to go 36 km upstream and 44 km downstream? Correct Answer 8 h

Given:

27km upstream and 33km downstream = 6 hours

36km upstream and 22km downstream = 6 hours

Formula:

Speed of boat = a kmph and Speed of stream = b kmph

Speed of upstream = (a - b) kmph

Speed of downstream = (a + b) kmph

Calculation:

⇒ 33/(a + b) + 27/(a - b) = 6

⇒ 22/(a + b) + 36/(a - b) = 6

Then,

⇒ 33/(a + b) + 27/(a - b) = 22/(a + b) + 36/(a - b)

⇒ 11/(a + b) = 9/(a - b) 

⇒ 11a - 11b = 9a + 9b

⇒ 2a = 20b

⇒ a = 10b

Then,

⇒ 33/(10b + b) + 27/(10b - b) = 6

⇒ 3/b + 3/b = 6

⇒ b = 1

⇒ a = 10

Speed downstream = 10 + 1 = 11 kmph

Speed upstream = 10 - 1 = 9 kmph

Then,

⇒ ? = 44/11 + 36/9 

⇒ ? = 4 + 4

⇒ ? = 8

∴ it will take 8 hours to go 36 km upstream and 44 km downstream.

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