Question

a boat goes 25km upstream and 33km downstream in 8 hours. The boat can also go40 km upstream and 77 km downstream in 15 hours. find the speed of the stream and that of the boat in still water.

Answer 1

25?......................

Answer 2

$\huge\mathfrak\red{Answer :}$


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

And downstream = (x+y) km

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

$\dfrac{25}{x - y}$ + $\dfrac{33}{x + y}$ = $8$ ....... (1)

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

$\dfrac{40}{x - y}$ + $\dfrac{77}{x + y}$= $15$ ......... (2)

Let 

x-y = $\dfrac{1}{a}$ and x+y = $\dfrac{1}{b}$

Then the eq. (1) and (2) is

25a + 33b = 8 ....... (3)
40a + 77b = 15 ....... (4)

Multiplying 16 by (3) and 10 by (4) then we get

400a + 528b = 128 ...... (5)
400a + 770b = 150 ..... (6)

Subtract eq. (5) from (6)

400a + 528b = 128 
400a + 770b = 150 [Change the signs]
_______________
000a - 242b = - 22
______________

$242b\:=\:22$

$b$ = $\dfrac{22}{242}$

$b$ = $\dfrac{1}{11}$

Put value of b in (3)

$25a\:+\:33$ × $\dfrac{1}{11}$ = $8$

$25a$ + $\dfrac{33}{11}$ = $8$

$25a$ = $8\:-\:3$

$25a\:=\:5$

$a$ = $\dfrac{5}{25}$

$a$ = $\dfrac{1}{5}$

So,

$x\:-\:y$ = $\dfrac{1}{a}$

$x\:-\:y$ = $5$ ...... (7)

$x\:+\:y$ = $\dfrac{1}{b}$

$x\:+\:y$ = $11$ ...... (8)

Solve (7) and (8) by elimination method

x - y = 5
x + y = 11
_________
2x + 0 = 16
_________

2x = 16

$\textbf{x = 8}$

Put value of x in (7)

8 - y = 5

- y = 5 - 8

- y = - 3

$\textbf{y = 3}$

So,

$\textbf{Speed of boat in still water}$

$\textbf{= 8 km/hr.}$

$\textbf{Speed of water in stream water}$

$\textbf{= 3 km/hr.}$

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