Formulate the problem as a pair of equations and then find their solutions.
A boat goes 30 km upstream and 44 km 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
Speed of boat upstream = (x – y) km/h
Speed of boat downstream = (x + y) km/h
a/c to question, boat goes 30 km upstream and 44 km downstream in 10 hours.
e.g., 30/(x - y) + 44/(x + y) = 10 .......(1)
again, In 13 hours it can go 40 km upstream and 55 km downstream.
e.g., 40/(x - y) + 55/(x + y) = 13 .......(2)
Let 1/(x - y) = P and 1/(x + y) = Q
then, equation (1), 30P + 44Q = 10
and equation (2), 40P + 55Q = 13
5(30P + 44Q) - 4(40P + 55Q) = 5 × 10 - 4 × 13
150P + 220Q - 160P - 220Q = 50 - 52
-10P = -2 => P = 1/5 = 1/(x - y)
(x - y) = 5 .......(3)
and 30 × 1/5 + 44Q = 10
44Q = 4 => Q = 1/11 = 1/(x + y)
(x + y) = 11 ........(4)
solve equations (3) and (4),
x = 8 and y = 3
hence, speed of the boat in still water is 8km/h and speed of the stream is 3 km/h
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.