A boat goes 21 km upstream and 18 km downstream in 9 hours. In 13 hours, it can go 30 km upstream and 27 km downstream. Determine the speed of the stream and that of the boat in still water. (Speed of boat in still water is more than the speed of the stream of river.)

Let the speed of the boat in still water be x km/hr and the speed of stream be y km/hr. It is necessary that x > y.

The speed of the boat in downstream = (speed of boat in still water + speed of stream) = (x + y) km/hr.

The speed of boat in upstream = (speed of boat in still water – speed of stream) = (x – y) km/hr.

Also, we know that

In the first case, it is given that boat goes 21 km upstream and 18 km downstream in 9 hours

⇒ Time taken by boat in upstream and downstream = 9 hr

In the second case, it is given that boat goes 30 km upstream and 27 km downstream in 13 hours

⇒ Time taken by boat in upstream and downstream = 13 hr

Putting these value in (i) and (ii), we get

21a + 18b = 9

30a + 27b = 13

So, the given equations transforms into linear equation in two variables

7a + 6b = 3 …. (iii)

30a + 27b = 13 … (iv)

Multiply (iii) by 9 and (iv) by 2,

63a + 54b = 27 …. (v)

60a + 54b = 26 … (vi)

Subtract (vi) from (v),

63a + 54b – 60a – 54b = 27 – 26

⇒ 3a = 1

Putting above value in (iii),

… (vii)

…. (viii)

Add above two equations,

x – y + x + y = 3 + 9

⇒ 2x = 12

⇒ x = 6

Putting x = 6 in (viii),

y = 9 – 6

⇒ y = 3