The speed of a stream is 9 km/h. A boat can cover a distance of 56 km downstream and 28 km upstream in 7 hours. Find the speed of the boat in still water (in km/h).

Given:

Speed of the stream = 9 km/h

Distance downstream = 56 km

Distance upstream = 28 km

Total time = 7 hours

Formula Used:

Speed of boat in still water = $\frac{Downstream speed + Upstream speed}{2}$

Downstream speed = Speed of boat in still water + Speed of the stream

Upstream speed = Speed of boat in still water - Speed of the stream

Calculation:

Let the speed of the boat in still water be x km/h.

Downstream speed = x + 9 km/h

Upstream speed = x - 9 km/h

Time taken to travel downstream = 56 / (x + 9)

Time taken to travel upstream = 28 / (x - 9)

Total time = 7 hours

⇒ 56 / (x + 9) + 28 / (x - 9) = 7

Multiply both sides by (x + 9)(x - 9):

⇒ 56(x - 9) + 28(x + 9) = 7(x + 9)(x - 9)

⇒ 56x - 504 + 28x + 252 = 7(x² - 81)

⇒ 84x - 252 = 7x² - 567

Rearrange the equation:

⇒ 7x² - 84x - 315 = 0

Divide the entire equation by 7:

⇒ x² - 12x - 45 = 0

Factorize the quadratic equation:

⇒ (x - 15)(x + 3) = 0

⇒ x = 15 or x = -3

Since speed cannot be negative, x = 15 km/h.

The speed of the boat in still water is 15 km/h.