Q1. A boat goes 30 km upstream and 44 km downstream in 10 hrs. In 13 hrs, it can go 40 km upstream and 55 km downstream. The speed of the boat in still water is
Answers
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.
Let, the speed of the stream be x km/hr
Speed of boat in still water =20 km/hr
∴Speed of boat with downstream 20+x km/hr
∴ Speed of boat with upstream 20−x km/hr
As per given condition
20−x48−20+x48=1
⟹48[20−x1−20+x1]=1
⟹[(20−x)(20+x)20+x−20+x]=481
⟹400−x22x=481
⟹96x=400−x2
⟹x2+96x−400=0
⟹x2+100x−4x−400
⟹x(x+100)−4(x+100)=0
⟹(x−4)(x+100)=0
Either, x=4 or x=−100
∵ Speed cannot be negative ∴x=4 km/hr is considered.
∴ the speed of the stream =4 km/hr