Question

A boat takes 10 hours to travel 30 km upstream and 44 km downstream but it takes 13 hours to travel 40 km upstream and 55 km downstream. Find speed of boat in still water and the speed of the stream.

Answer 1

speed of boat=x
speed of stream=y
speed upstream=x-y
speed downstream=x+y
according to first condition
time(upsteam)+time(downstream)=10
30/(x-y) + 44/(x=y)=10 ..........(1)    {time=distance by speed}
similarly
40/(x-y) + 55/(x+y)=13................(2)
solve these 2 equations and find the answers

Answer 2

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

Upstream speed = speed of boat - speed of stream = x - y [assumption values 'x' & 'y']
Down stream speed = x + y

Given 30/x-y + 44/x+y = 10 hours...... (i)
40/x-y + 55/x+y = 13 hours.......(ii)

Multiply eq.(i) by 4 && eq.(ii) by 3
120/x-y + 176/x+y = 40......(iii)
120/x-y + 165/x+y = 39......(iv)

(iii) - (iv)
11/x+y = 1
x+y = 11......(a)
Substitute (a) in (iii)
120/x-y + 176/11 = 40 
120/x-y + 16 = 40
120/x-y = 24
x-y = 120/24 =5
x-y = 5
x+y = 11
add above 2=== 2x = 16
x = 8 kmph
8+y = 11
y= 3 kmph

Hence speed of boat = 8 kmph
Speed of stream = 3 kmph
Hope this helps