Question

A boat can row 18 km downstream and back in 8 hours. If the speed of boat is increased to twice its previous speed, it can row same distance downstream and back in 3.2 hours. find speed of boat in still water​

Answer 1

Given :- A boat can row 18 km downstream and back in 8 hours. If the speed of boat is increased to twice its previous speed, it can row same distance downstream and back in 3.2 hours.

Solution :-

Let speed of boat in still water is x km/h and speed of current is y km/h .

so,

→ 18/(x + y) + 18/(x - y) = 8

→ 1/(x + y) + 1/(x - y) = 8/18

→ (x - y + x + y)/(x² - y²) = 4/9

→ 2x/(x² - y²) = 4/9

→ x/(x² - y²) = 2/9

→ 9x = 2x² - 2y² ------ Eqn.(1)

and,

→ 18/(2x + y) + 18/(2x - y) = 3.2 = 3(1/5) = 16/5

→ 1/(2x + y) + 1/(2x - y) = 16/5*18

→ (2x + y + 2x - y) /(4x² - y²) = 8/45

→ 4x/(4x² - y²) = 8/45

→ 180x = 32x² - 8y² ---------- Eqn.(2)

dividing both equations we get,

→ 9x/180x = 2(x² - y²)/8(4x² - y²)

→ 1/20 = (x² - y²)/4(4x² - y²)

→ 1/5 = (x² - y²)/(4x² - y²)

→ 4x² - y² = 5x² - 5y²

→ 5y² - y² = 5x² - 4x²

→ 4y² = x²

→ x = 2y .

putting this value in Eqn.(1),

→ 9(2y) = 2(2y)² - 2y²

→ 18y = 8y² - 2y²

→ 18y = 6y²

→ y = 3 km/h .

therefore,

→ The speed of boat in still water = x = 2y = 2 * 3 = 6 km/h (Ans.)

Learn more :-

शांत जल में एक नाव को अपने गंतव्य स्थान तक पहुंचने और वहां

से अपने प्रारंभिक स्थान पर वापस आने में कुल 15 घंटे लगते हैं।...

https://brainly.in/question/21974439

A man can row 40 km upstream and 60 km downstream in 13 hours. He can also tow 50 km pamat In the given context, what is ...

https://brainly.in/question/37472733