Question

the boat goes 30 kilometre upstream and 44 km downstream in 10 hours in 13 hours it can go 40 kilometre upstream and 55 km downstream determine the speed of stream of and the of the boat in still water

Answer 1

Let speed of the boat be x km/h

speed of the stream be y km/h

then the speed of boat downstream =(x+y)km/h

the speed of boat upstream =(x-y)km/h
30/x-y +44/x+ y =10 _________eq 1

40/ x-y + 55/ x+y =13 _____________eq 2

put 1/ x-y=u and 1/x+ y =v

30u + 44v = 10
40u +55 v=13

using cross multiplcitation
methods


u/44 (- 13 )- 55( - 10) = v/40( - 10) - 30 (- 13) = 1 / 30 (55 )- 44(40)
u/- 22 =4 /- 10 =1/ -110
u = 1 / 5 v= 1 /11
now put this value of U and V in equation 3 we get
1/x-y =1/5 and 1/x+y= 1/11
x-y=5and x+y=11

adding this equation we get

2x = 16
x = 8


subtracting the equation in 6 we get

2 Y = 6
Y = 3

Answer 2

Hello !

Speed of boat = x km/hr
Speed of stream = y km/hr

While going upstream ,
speed = (x - y) km/hr
distance = 30 km
time = distance / speed = 30 / x-y  hours

While going downstream ,
speed = (x + y) km/hr
distance = 44 km
time = distance / speed = 44 /x + y hours

Total time = 10 hr
30 / x-y   + 44 /x + y  = 10         

Let ,
1/x -y = u , 1/x+y = v
the equation becomes :-
30u + 44v = 10              -----> [1]

----------------------------------

While going upstream ,
speed = (x - y) km/hr
distance = 40 km
time = distance / speed = 40 / x-y  hours


While going downstream ,
speed = (x + y) km/hr
distance = 55 km
time = distance / speed = 55 /x + y hours

Total time = 13 hrs

40 / x-y + 55 /x + y = 13

Let ,

1/x -y = u , 1/x+y = v
the equation becomes :-

40u + 55v = 13       ----> [2]

-----------------------------------------

solving equations 1 and 2 ,

3 x (40u + 55v = 13 )
4 x (30u + 44v = 10)  

120 u + 165v = 39   ----> [3]
120u + 176v = 40    ----> [4]

Subtracting equation 3 from 4 , we get ,

11v = 1
 v = 1/11

also ,
40u + 55v = 13
40u + 55 x 1/11 = 13

40u + 5 = 13

40u = 13 -5

40u = 8

u = 8/40 = 1/5

given ,


1/x -y = u 
1/x -y = 1/5

cross multiplication ,
x -y = 5

similarly,
 1/x+y = v

x +y = 11

solving ,

    x +y = 11
+  x - y = 5
--------------

2x = 16

x = 8

x -y = 5

8 -y = 5

y = 3

==============================

x = 8 , y = 3

Speed of boat = 8 km/hr
speed of current = 3 km/hr