Question

A boat takes 6 hour to travels 36km downstream and 24km upstream.it takes 9 hour to travel 48km downstream and 40 km upstream find the speed of the boat in still water and the speed of stream

Answer 1

            Total Time =
Upstream distance/upstream speed + Downstream dist/downstream speed  

Let speed of boat=x
Let speed of stream=y
Upstream speed = speed of boat - speed of stream = x - y 
Down stream speed = speed of boat + speed of stream = x + y

Given 36/x+y + 24/x-y = 6 hours...... (i)
48/x+y + 40/x-y = 9 hours.......(ii)

Multiply eq.(i) by '5' and eq.(ii) by '3'
180/x+y + 120/x-y = 30.....(iii)
144/x+y + 120/x-y = 27.....(iv)
Subtract above equations:
36/x+y = 3
x+y = 12.....(a)
(a) in (iv)
144/12 + 120/x-y = 27
12 + 120/x-y = 27
120/x-y = 15
x-y = 8
x+y = 12
Adding both:
2x = 20
x=10
10+y = 12
y=2

Speed of boat in still water = 10 kmph
Speed of stream = 2 kmph
Hope this helps

Answer 2

Answer:

Step-by-step explanation:

Upstream distance/upstream speed + Downstream dist/downstream speed  

Let speed of boat=x

Let speed of stream=y

Upstream speed = speed of boat - speed of stream = x - y 

Down stream speed = speed of boat + speed of stream = x + y

Given 36/x+y + 24/x-y = 6 hours...... (i)

48/x+y + 40/x-y = 9 hours.......(ii)

Multiply eq.(i) by '5' and eq.(ii) by '3'

180/x+y + 120/x-y = 30.....(iii)

144/x+y + 120/x-y = 27.....(iv)

Subtract above equations:

36/x+y = 3

x+y = 12.....(a)

(a) in (iv)

144/12 + 120/x-y = 27

12 + 120/x-y = 27

120/x-y = 15

x-y = 8

x+y = 12

Adding both:

2x = 20

x=10

10+y = 12

y=2

Speed of boat in still water = 10 kmph

Speed of stream =2kmph