The speed of a stream is 8 km/h. A boat can go 19 km downstream and 9 km upstream in 4 hours. What is the speed (in km/h) of the boat in still water?

Given:

Speed of the stream = 8 km/h

Downstream distance = 19 km

Upstream distance = 9 km

Total time = 4 hours

Formula used:

Time = Distance / Speed

Calculation:

Speed of the boat in still water = x km/h

Speed downstream = (x + 8) km/h

Speed upstream = (x - 8) km/h

Time downstream = 19 / (x + 8)

Time upstream = 9 / (x - 8)

⇒ Total time = Time downstream + Time upstream

⇒ 4 = 19 / (x + 8) + 9 / (x - 8)

⇒ Multiply both sides by (x + 8)(x - 8) to eliminate the denominators:

⇒ 4(x + 8)(x - 8) = 19(x - 8) + 9(x + 8)

⇒ 4(x² - 64) = 19x - 152 + 9x + 72

⇒ 4x² - 256 = 28x - 80

⇒ 4x² - 28x - 176 = 0

⇒ Divide the equation by 4:

⇒ x² - 7x - 44 = 0

Solving this quadratic equation:

Using the quadratic formula: x = [-(-7) ± √((-7)² - 4 × 1 × (-44))] / 2 × 1

⇒ x = [7 ± √(49 + 176)] / 2 = [7 ± √225] / 2 = [7 ± 15] / 2

⇒ x = (7 + 15) / 2 = 22 / 2 = 11

∴ The speed of the boat in still water = 11 km/h