Question

A boat takes 6hours to travel 36km downstream & 24 km upstream. It takes 9 hours to travel 48 km downstream & 40 km to upstream. Find the the speed of stream & that of boat in still water

Answer 1

Step-by-step explanation:

let the speed of boat be x and that of stream be y

therefore speed of boat while going downstream be x + y

the speed of boat while going upstream be x - y

therefore atq

36/(x+y) +24/(x-y)=6..................eq.1

and

48/(x+y)+40/(x-y)=9....................eq.2

now let 1/x+y be a and 1/x-y be b

therefore

36a+24b = 6

and

48a + 40b = 9

now solving the equations we get

a=1/12

and

b=1/8

therefore

x+y=12

and

x-y=8

again solving for x and y we get

x=10

and

y=2

hence

speed of boat = 10

and

speed of stream=2

Answer 2

Answer:

let speed of boat be x

let speed of stream be y

upstream speed =x-y

downstream speed =x+y

given 36/x+y +24/x-y=6hours...1

48/x+y +40/x-y=9hours.....2

Multiply eq 1 with 3 and 2 with 3

180/x+y +120/x-y=30hours....3

144/x+y +120/x-y=27hours.....4

subtract

x+y=12........a

substitute a in 4

144/12+120/x-y=27

12+120/x-y=27

120/x-y =15

x-y=8

x+y=12

add both of them

2x=20

x=10

10+y=12

y=2

speed of boat in still water=10kmph

speed of stream =2kmph