A boat goes 30 km upstream and 44 km downstream in 10 hours.It can go 40 km upstream and 55 km downstream in 13 hours. Find the speed of the stream and that of the boat in still water.
Answers
and that speed of river = y km/hr
now while going upstream speed of man = x-y as boat goes against river current
and while going downstream speed of man = x+y as he goes along river current
let us assume p= 1 / x+y and q = 1 / x-y for simplicity
so A/Q 30/x-y + 44 / x+y = 10
that becomes 30q + 44p = 10 ...........(1)
and 40/x-y + 55 /x+y = 13
⇒ 40q +55p = 13 ..........(2)
on solving we get q = 1/5 and p = 1/11
that produces x-y = 5 x +y = 11
again solving simultaneous equation fetches x= speed of boat = 8 km/hr
y = speed of river = 3 km/hr
hope this helps .
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.