0. 28. A boat goes 30 km upstream and 44 km
downstream in 10 hours. The same boat goes 40 km
upstream and 55 km downstream in 13 hours. On this
information, some students guessed the speed of the boat
in still water as 8-5 km/h and speed of the stream as 3-8
km/h. Do you agree with their guess ?*
Answers
Step-by-step explanation:
Let the speed of boat still in water be xkm/hr.
speed of stream be ykm/hr.
According to the problem,
30/x-y + 44/x+y. =10. ----1
According to the problem,
40/x-y + 55/x+y. =13. -----2
let
1/x-y=p
1/x+y=q
so,
30p+44q= 10 ------1*4
40p+55q= 13 ------2*3
- - -
------------------------------
120p+176q= 40
-120p -165q=-39
------------------------------
11q=1
q=1/11
1/x+y=1/11
x+y=11. --------3
30p+44q=10
30p+44(1/11)=10
30p+4=10
30p=10-4
=6
so,
p=6/30
=1/5
1/x-y=1/5
x-y=5 --------4
from 3 and 4
x+y=11
x-y =5
------------------
2x=16
x=8km/hr
y=3km/hr.
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.