Question

The speed of boat in still water is 12km/h. It can goes 36 km upstream and return to downstream to the original point in 8 hours. Find the speed of stream.​

Answer 1

Solution:

Given:

• Speed of boat in still water = 12 km/h
• Total distance = 36 km

To Find:

• Speed of stream.

Let, the speed of the stream = x km/h

So, Speed of boat in downstream = (12 + x) km/h

Speed of boat in upstream = (12 - x) km/h

Now, According to question,

$\implies \sf \dfrac{36}{12+x}+\dfrac{36}{12-x}=8\\ \\ \\ \implies \sf \dfrac{432-36x+432+36x}{144-x^{2}}=8\\ \\ \\ \implies \sf \dfrac{864}{144-x^{2}}=8\\ \\ \\ \implies \sf 1152-8x^{2}=864\\ \\ \\ \implies 8x^{2}=1152-864\\ \\ \\ \implies \sf 8x^{2}=288\\ \\ \\ \implies \sf x^{2}=\dfrac{288}{8}\\ \\ \\ \implies x^{2}=36\\ \\ \implies x=\sqrt{36}\\ \\ \implies \sf x = \pm 6$

As we know that distance cannot be negative. So x = 6

Hence, Speed of stream = 6 km/h.