Question

A motor boat can travel 30 km upstream and 28km downstream in 7hours. It can travel

21km upstream and return in 5hours. Find the speed of the boat in still water and the

speed of the stream

Answer 1

Hey mate here is your answer☺️✌️

This kind of questions follows the same pattern:

Let the speed of the boat in still water = x km/hr.

Let the speed of the stream = y km/hr.

Speed upstream = x - y.

Speed Downstream = x + y.


Now,

Given that boat can travel 30km upstream and 28km downstream in 7 hours.

30/x-y + 28/x+y = 7 

Let 1/x - y = a and 1/x + y = b

30a + 28b = 7        ---------------------------- (1).

Also, Given that it can travel 21 km upstream and return in 5 hours.

21/x - y + 21/x + y = 5

Let 1/x - y = a and 1/x + y = b 

21a + 21b = 5   ------------------------ (2)


On solving (1) * 21 & (2) * 28, we get

630a + 588b = 147

588a + 588b = 140
-----------------------------
42a = 7

a = 1/6.

Substitute a = 6 in (1), we get

30a + 28b = 7

30(1/6) + 28b = 7

5 + 28b = 7

28b = 7 - 5

28b =2

b = 2/28

b = 1/14.

We know that, 

a = 1/x - y

1/6 = 1/x - y

x - y = 6   ----------- (3)


We know that,

b = 1/x + y

1/14 = 1/x + y

x + y = 14   ------------ (4).


On solving (3) & (4), we get

x + y = 14

x - y = 6

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

2x = 20

x = 10


Substitute x = 10 in (4), we get

x + y = 14

10 + y = 14

y = 14 - 10

y = 4.


Therefore the speed of the boat in still water = 10km/hr.

Therefore the speed of the stream = 4km/hr.

NOTE: Sorry, for making such a lengthy calculations.

Hope this helps!  --------------- Good Luck
☺️✌️☺️✌️☺️✌️☺️✌️☺️

Answer 2

let the speed of the boat in still water be X km/he
let the speed of the stream be y km/hr
then the speed of the boat in downstream=(X+y)km/hr
speed of the boat in upstream=(x-y)km/hr
also,. time=distance/speed

when the boat goes 30 km upstream,let time taken T1
T1=30/x-y
when the boat goes 44 km downstream late time taken T2 T2 =44/X+y
therefore we get the equation
30/x-y+44/X+y=10

in 13 hours it can go 40 km upstream and 55 km downstream we get the equation
40/x-y+55/X+y=13
let 1/x-y=u and 1/X+y=v

substituting these values we get,
30u + 44v = 10
30u+44v-10=0____i
40u+55v=13
40u+55v-13=0_____ii

by cross- multiplication of equation i and ii
we get u = 1/5,v=1/11

i.e., x-y=5 and X+y=11

adding the equation 2x= 16
X=8