Q. 34.0( 8 Votes )

# A boat goes 21 km

Answer :

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

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