Question

The boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of stream and that of the boat in still water.

Answer 1

SOLUTION :  

Let the speed of the boat in still water be x km/hr and the speed of the stream be y km/hr

Speed upstream = (x -y) km/hr

Speed downstream =(x + y) km/hr  

Now,

Case : 1

Time taken to cover 30 km upstream = 30/ (x−y) hrs

[ Time = distance/speed]

Time taken to cover 44 km downstream =44/(x+y) hrs

Given : The total time of journey = 10 hours

30/(x−y) +  44(x+y)= 10 …………...(1)

Case : 2

Time taken to cover 40 km upstream =  

40/( -y) hrs

Time taken to cover 55 km downstream =  

55/(x+y) hrs

Given :  The total time of journey = 13 hours

40/(x−y) + 55/(x+y) = 13............(2)

Putting 1/(x−y) and 1/(x+y) in equation (1) and (2)  

30u + 44v = 10

40u + 55v = 13

30u + 44v -10 = 0 ………….(3)

40u + 55 -13 = 0…………….(4)

Solving these equations by cross multiplication we get,  

u/44 × -13−55 ×-10 = −v/30× -13− 40×-10 = 1/30×55−40×44

u/ - 572 + 550 = - v/ -390+400 = 1/1650 - 1760

u/ -22 = -v / 10 = 1/ -110

u/ -22  = 1/ -110

u = −22/−110

u  = 1/5

-v / 10 = 1/ -110

v  = 10/110  

v = 1/11

Now,

1/(x−y) = 1/5

x - y = 5………………(5)

1/(x+y) = 1/11

x + y 11.....................(6)

On adding eq 5 & 6

x - y = 5

x + y = 11

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

2x = 16

x = 16/2

x = 8

On Putting x= 8 in equation 6,

x + y = 11

8+ y = 11

y = 11 – 8

y = 3

Hence, speed of boat in still water is 8 km/hr &  Speed of the stream is 3 km/hr.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

let the speed of the stream be u kmph
and speed of the boat be v kmph

speed upstream will be = (v-u)kmph

speed downstream will be = (v+u)kmph

30km upstream in time duration = 30/(v-u) hrs

44km downstream in time duration = 44/(v+u) hrs
44/(v+u) + 30 /(v-u) = 10hrs ..... (i)

Similarly,
40/(v-u) +55/(v+u) = 13hrs

multiply with 3/4,
30/(v-u) + 165/4 (v+u) = 39/4 hrs .....(ii)

Now (i)-(ii)
(44-165/4)/(v+u) = 10-39/4 =1/4
or, v+u =11 .... (a)
Substitute this in eq (i)
44/11 +30/(v-u) = 10
4 + 30/(v-u) = 10
v-u = 5 ....... (b)
Solving eq (a) and (b) , we get
v=8kmph and u = 3kmph
Hence , speed of stream and that of boat are 3kmph and 8kmph respectively.
hope it helps you.