Question

please someone solve this example 10

Answer 1

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

Note: speed when going upstream is x-y and when going downstream is x+y.

We know that
Distance = speed * time
Therefore,
Time= distance / time

According to the given conditions,

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

Let 1/x-y be 'a' and 1/x+y be 'b'

Therefore our equations become....

30a+44b=10
15a+22b=5........(iii) (dividing by 2)
40a+55b=13......(iv)
Now multiply equation iii by 40 and equation iv by 15


We get....

600a+880b=200
600a+825b=195

Solving these two equations by elimination method,

600a+880b=200
600a+825b=195
...............................
55b=5
b=1/11
Substituting this value in equation iii

15a+22*1/11=5
15a= 5-2= 3
a= 1/5

Since we have assumed a and b to be 1/x-y and 1/ x+y respectively.

Therefore 1/x-y=1/5
and 1/x+y=1/11

Reciprocating,

We get x-y = 5
Therefore x= 5+y........(v)
x+ y = 11...........(vi)

Substituting (v) in (vi)

5+y+y=11
5+2y=11
2y=6
y=3
Substituting y=3 in (v)

x=8

Therefore speed of stream is 3 km/hr and speed of boat in still water is 8km/hr. ..

Hope this helped..... Plz mark as brainliest....