Question

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

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 = 12 (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