The speed of a stream is 6 km/h. A boat can go 56 km downstream and 39 km upstream in 7 hours. What is the speed (in km/h) of the boat in still water?

Correct option is B

Given:

Speed of stream = 6 km/h

Downstream distance = 56 km

Upstream distance = 39 km

Total time = 7 hours

Formula Used:

Downstream speed = boat speed + stream speed

Upstream speed = boat speed − stream speed

Total time = time downstream + time upstream

Time = $$\frac{Distance}{Speed}$$​​

Solution:
Let speed of boat in still water = x km/h
Then,

Downstream speed = x + 6

Upstream speed = x – 6

Now,

​$$\frac{56}{x+6} + \frac{39}{x-6} = 7 \\ 56(x-6) + 39(x+6) = 7(x+6)(x-6) \\ 56x - 336 + 39x + 234 = 7(x^2 - 36) \\ 95x - 102 = 7x^2 - 252 \\ 7x^2 - 95x - 150 = 0 \\ x = \frac{95 \pm \sqrt{(-95)^2 - 4 \times 7 \times (-150)}}{2 \times 7} \\ x = \frac{95 \pm \sqrt{9025 + 4200}}{14} = \frac{95 \pm \sqrt{13225}}{14} \\\ \\ x = \frac{95 + 115}{14} = \frac{210}{14} = 15 \\\ \\ x = \frac{95 - 115}{14} = \frac{-20}{14} = -\frac{10}{7} \quad (\text{discard negative}) \\$$ 

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