Question

Hølä !!!

An 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 the stream and that of the boat in still water ?


Cläßß => 10th

Chap => Pair of linear equation in two variables ?

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Answer 1

Solutions :-

Given :
An 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.

Let the speed of boat be x km/hr
And the speed of stream be y km/hr

So,
Upstream speed = (x - y) km/hr
Downstream speed = (x + y) km/hr

We know that,
Time = Distance / Speed

According to the question,

30/(x - y) + 44/(x + y) = 10 ______(i)
40/(x - y) + 55/(x + y) = 13 ______(ii)

Let 1/(x + y) be u
1/(x - y) be v


So,
30v + 44u = 10 ___(iii)
40v + 55u = 13 ___(iv)


[30v + 44u = 10] × 4 => 120v + 176u = 40 ___(v)
[40v + 55u = 13] × 3 => 120v + 165u = 39 ___(vi)


Subtract equation (vi) from (v) we get,

(120v + 176u) - (120v + 165u) = 40 - 39
=> 120v + 176u - 120v - 165u = 1
=> 11u = 1
=> u = 1/11


Putting the value of u in equation (iii) we get,

30v + 44 × 1/11 = 10
=> 30v + 4 = 10
=> 30v = 10 - 4
=> 30v = 6
=> v = 6/30= 1/5


Now,
1/(x + y) = u = 1/11
=> x + y = 11 ____(vii)

1/(x - y) = u = 1/5
=> x - y = 5 _____(viii)


Adding equation (vii) and (viii) we get,

=> (x + y) + (x - y) = 11 + 5
=> x + y + x - y = 16
=> 2x = 16
=> x = 16/2 = 8


Putting the value of x in equation (viii),

8 - y = 5
=> - y = 5 - 8
=> y = 3


Hence,
Speed of the boat = 8 km/hr
And the speed of stream = 3 km/hr

Answer 2

Answer:

Speed of stream = 3 km / hr.

Speed of boat in still water = 8 km / hr.

Step-by-step explanation:

Let the speed of the boat in still water be a km / hr and stream be b km / hr

For upstream = a - b

For downstream = a + b

We know :

Speed = Distance / Time

Case 1 .

10 = 30 / a - b + 44 / a + b

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

30 x + 44 y = 10 ... ( i )

Case 2 .

13 = 40 / a - b + 55 / a + b

40 x + 55 y = 13 ... ( i )

Multiply by 4 in ( i ) and by 3 in ( ii )

120 x + 176 y = 40

120 x = 40 - 176 y ... ( iii )

120 x + 165 y = 39

120 = 39 - 165 y ... ( iv )

From ( iii )  and  ( iv )

40 - 176 y = 39 - 165 y

11 y = 1

y = 1 / 11

120 x = 40 - 176 y

120 x = 40 - 176 / 11

x = 1 / 5

Now :

1 / a - b = 1 / 5

a - b = 5

a = 5 + b ... ( v )

1 / a + b = 1 / 11

a + b = 11

a = 11 - b ... ( vi )  

From ( v  ) and ( vi )

11 - b = 5  + b

2 b = 6

b = 3

a = 5 + b

a = 5 + 3

a = 8

Hence we get answer.