A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it cango 40 km upstream and 55 km downstream. Determine the speed of thestream and that of the boat in still water?

Let the speed of the boat in still water be x km/hr
and the speed of the stream be y km/hr.
Speed of the boat while going downstream = (x + y) km/hr.
and speed of the boat while going upstream = (x - y) km/hr
Condition 1:
A boat goes 30 km upstream and 44 km downstream in 10 hrs.
Time taken to go upstream by the boat =
and time taken to go downstream by the boat = ⇒ … (i)
Condition 2:
A boat goes 40 km upstream and 55 km downstream in 13 hrs.
Time taken to go upstream by the boat =
and time taken to go downstream by the boat = ⇒ … (ii)
The L.C.M. of 44 and 55 is 440.
∴ Multiplying (i) by 5 and (ii) by 4

⇒ … (iii)

⇒ … (iv)
(-)  (-)       (-)
____________

____________
-10 = -2 (x - y)
5 = x - y
. ^. . x - y = 5 … (v)
Substituting x - y = 5 in (i)
30/5 + = 10
6 + = 10

= 10 – 6

= 4
44 = 4 (x + y)
11 = x + y
. ^. . x + y = 11… (vi)
Adding (v) and (vi)
x - y = 5
x + y =  11
2x     =  16
x = 8
Substituting x = 8 in (v)
8 - y = 5
-y = 5 -8
-y = -3
y = 3
. ^. .The speed of the stream is 3km/hr and the speed of the boat in still water is 8km /hr.