a boat goes 30 km upstream and 44km downstream in 10 hours. in 13 hours, it can go 40 km upstream and 55 km downstream. determine the speed of the stream and that of the boat in still water.
Answers & Comments
paradkar
And then solve the simultaneous equation by substitution and then resubstitute to get the final answer
Answers & Comments
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.