a boat goes upstream 30 km and downstream 44 km in 10 hrs. it also goes upstream 40 km and downstream 55 km in 13 hrs. find the speeds of the stream and the boat.
Answers
let the speed of the steam be y
the speed of the boat upstream = (x-y) kmph
the speed of the boat downstream = (x+y) kmph
then,
30/(x-y)+44/(x+y)=10
& let 1/(x-y) = a & 1/(x+y)=b
you get,
30a+44b=10..............(1)
similarly you get the other equation
40a + 55 b=13..............(2)
multiply (1) by 4 and (2) by 3 we get
120a+176b=40.............(3)
120a+165b=39..............(4)
subtract eqn. (4) - eqn. (3)
we get b= 1/11
and then putting the value in the equation in
30a+4=10
hence a=1/5
now b=1/(x+y)=1/11
or
x+y=11............(5)
and
a=1/(x-y)=1/5
or
x-y=5.........(6)
adding eqn.(5)& eqn.(6)
we get
2x=16
or x = 8
then putting the value in eqn 5 we get
8+y=11 or
y= 3
hence the speed of the boat=8km
& the speed of the steam = 3km
hope this helps you :D
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.