Question

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.)

Answer 1

HELLO DEAR,

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 6 and the speed of the strean be 3.
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I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

hey

here is the answer

see in attachment

hope it helps

thanks