In 10 hours Mayur rows 30 kms upstream and 44 kms downstream. Also he travels 40 kms upstream and 55 kms downstream in 13 hours. What is speed of the boat in still water?

8 km/hr

Let,

Speed of boat in still water - x = ?

Speed of stream/current - y

Upstream speed: x - y = U

Downstream speed: x + y = D

Speed = \(\frac{ Distance}{ Time}\)

Time = \(\frac{ Distance}{ Speed}\)

According to the question:

\(\frac{30 }{ U}\) + \(\frac{44 }{D}\) = 10 ------1st equation

\(\frac{40 }{ U}\) + \(\frac{55}{ D}\) = 13 ------2nd equation

Solving the 1st equation:

\(\frac{ \text{30D + 44U}}{ UD}\) = 10

30D + 44U = 10UD 

Multiplying by 13 on both the sides:

390D + 572U = 130UD ------------(3)

Solving the 2nd equation:

\(\frac{ \text{40D + 55U}}{ UD}\) = 13

40D + 55U = 13UD 

Multiplying by 10 on both the sides:

400D + 550U = 130UD -------------(4)

From equation (3) and (4), we can deduce that:

390D + 572U = 400D + 550U 

22U = 10D

\(\frac{U }{ D}\) = \(\frac{10 }{22 }\)

\(\frac{U }{ D}\) = \(\frac{5 }{11}\)

So, we can say x + y = 11 and x - y = 5

After solving the values of x and y is 8 and 3.

Thus x i.e. speed of boat in still water is 8 km/hr