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According to the question, the motorboat takes 30 minutes more to go 24 km upstream than to cover the same distance downstream. Let, the speed of the water = x km/h So, 24/(20 - x) = 24/(20 + x) + (1/2) [∵ 30 minutes = 1/2 hour] ⇒ 24/(20 - x) - 24/(20 + x) = (1/2) => {24(20+x) - 24(20-x)}/(400 - x2) = 1/2 => 24(20+x-20+x)/400 - x2 = 1/2 => (24 x 2x)/400-x2 = 1/2 ⇒ 400 - x2 = 96x ⇒ x2 + 96x - 400 = 0 ⇒ x2 + 100x - 4x - 400 = 0 ⇒ x (x + 100) - 4 (x + 100) = 0 ⇒ (x + 100) (x - 4) = 0 ⇒ x + 100 = 0 ⇒ x = -100 ["-" is neglacted] ⇒ x - 4 = 0 ⇒ x = 4 ∴ The speed of the water = 4 km/h The speed of the motorboat in still water increased 2 km/h = 20 + 2 = 22 km/h The time for 39 km downstream and 30 km upstream = 39/(22 + 4) + 30/(22 - 4) hours = (39/26) + (30/18) hours = 3/2 + 5/3 hours = 19/6 hours = (19/6) × 60 minutes = 190 minutes = 3 hours 10 minutes
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