Question

the boat goes 25 kilometre upstream and 33 km downstream in 8 hours it can also go 40 kilometre upstream and 77 km downstream in 15 hours find the speed of the stream and that of boat in still water plzz help

Answer 1

Let speed of the boat in still water = x km/h
Speed of stream = y km/h
Speed of the boat upstream = (x-y)km
Speed of the boat downstream = (x+y)km

Since time taken by the boat in 25 km upstream and 33km downstream is 8hrs,

(25/x-y) + (33/x+y) = 8................1

Also,time taken by the boat in 40 km upstream and 77km downstream is 15hrs,

(40/x-y) + (77/x+y) = 15..............2

Let x-y = 1/a and x+y = 1/b, then the equations 1 and 2 become
25a + 33b = 8............3
40a + 77b = 15............4

Multiplying 16 with (3) and 10 with (4),we get;
400a + 528b = 128........5
400a + 770b = 150........6

Subtracting 5 from 6,we get;
242b = 22
=> b = 22/242 = 1/11

Substituting b = 1/11 in (3),we get;
25a + 33x 1/11 = 8
=>25a = 8-3 =5
=> a = 5/25 =1/5

So,   x-y = 5  ........7
 and x+y = 11 ........8

On adding 7 and 8, we get;
2x = 16
=> x = 8

Substituting x=8 in (8),we get;
8 + y =11
=>y = 3


Hence,the speed of the boat in still water is 8 km/h and the speed of the stream is 3 km/h.

Hope it helps!

Answer 2

Step-by-step explanation:

et speed of the boat in still water = x km/h

Speed of stream = y km/h

Speed of the boat upstream = (x-y)km

Speed of the boat downstream = (x+y)km

Since time taken by the boat in 25 km upstream and 33km downstream is 8hrs,

(25/x-y) + (33/x+y) = 8................1

Also,time taken by the boat in 40 km upstream and 77km downstream is 15hrs,

(40/x-y) + (77/x+y) = 15..............2

Let x-y = 1/a and x+y = 1/b, then the equations 1 and 2 become

25a + 33b = 8............3

40a + 77b = 15............4

Multiplying 16 with (3) and 10 with (4),we get;

400a + 528b = 128........5

400a + 770b = 150........6

Subtracting 5 from 6,we get;

242b = 22

=> b = 22/242 = 1/11

Substituting b = 1/11 in (3),we get;

25a + 33x 1/11 = 8

=>25a = 8-3 =5

=> a = 5/25 =1/5

So,   x-y = 5  ........7

 and x+y = 11 ........8

On adding 7 and 8, we get;

2x = 16

=> x = 8

Substituting x=8 in (8),we get;

8 + y =11

=>y = 3

Hence,the speed of the boat in still water is 8 km/h and the speed of the stream is 3 km/h.

Hope it helps!