Question

A boat goes 21 km upstream and 18 km down stream in 9 hours, In 13 hours if can go 30 km upstream and 27 km downstream.Find the speed of boat and stream.​

Answer 1

Answer:

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Let the speed of the boat be x and the speed of the strean be y

Then speed of the boat in upstream = (x - y) km/hr

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

Then 21/(x - y) + 18/(x + y) = 9

and 30/(x - y) + 27/(x + y) = 13

Let 1/(x - y) = a and 1/(x + y) = b

therefore,

7a + 6b = 3----------( 1 )

10a + 9b = 13/3---------( 2 )

From---------( 1 ) &---------( 2 )

multiply ------( 1 ) by 9 & -----( 2 ) by 6.

63a + 54b = 27

60a + 54b = 26

————————

3a = 1

a = 1/3 [ put in------( 1 )]

7(1/3) + 6b = 3

⇒7 + 18b = 9

⇒18b = 2

⇒b = 1/9

now, put a = 1/(x - y) = 1/3

⇒x - y = 3----------( 3 )

b = 1/(x + y) = 1/9

⇒x + y = 9----------( 4 )

From--------( 3 ) &--------( 4 )

x - y = 3

x + y = 9

————–

2x = 12

x = 6 [ put in --------( 3 )]

we get,

6 - y = 3

y = 6 - 3

y = 3

hence, the speed of the boat be 6km/h and the speed of the strean be 3.km/h