The boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of stream and that of the boat in still water.

To find: the speed of stream and that of the boat in still water.

Explanation:

Speed = distance/time

Let the speed of boat be ‘a’ and speed of stream be ‘b’

Relative speed of boat going upstream = a – b

Relative speed of boat going downstream = a + b

we know,

boat goes 30 km upstream and 44 km downstream in 10 hours.

In 13 hours, it can go 40 km upstream and 55 km downstream

Now take,

Eq. 1 and 2 becomes

⇒ 30 u + 44 v = 10

Take 2 common out of above equation

⇒ 15 u + 22 v – 5 = 0 ..... (3)

and

40 u + 55 v – 13 = 0 ..... (4)

Solve the equations by cross multiplication method,

Method of cross multiplication

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

Here a₁= 15 a₂ = 40

b₁= 22 b₂ = 55

c₁= –5 c₂ = –13

So, for the given values,

⇒ a– b = 5 .... (4)

a + b = 11 .... (5)

Add eq 4 and 5 to get

a – b + a + b = 5 + 11

⇒ 2a = 16

⇒ a = 8

Substitute value of a in eq 4 we get,

8 – b = 5

⇒ b = 8 – 5

⇒ b = 3

Speed of boat = 8 km/hr and speed of stream = 3 km/hr