If a motor boat can travel 30 km upstream and 28 downstream in 7h it can travel 21 km upstream and return in 5h find the speed of boat in still water and the speed of the stream
Answers
Answer:
This kind of questions follows the same pattern:
Let the speed of the boat in still water = xkm/hr.
Let the speed of the stream = ykm/hr.
Speed upstream = x - y.
Speed Downstream = x + y.
Now,
Given that boat can travel 30km upstream and 28km downstream in 7 hours.
30/x-y + 28/x+y = 7
Let 1/x - y = a and 1/x + y = b
30a + 28b = 7 ---------------------------- (1).
Also, Given that it can travel 21 km upstream and return in 5 hours.
21/x - y + 21/x + y = 5
Let 1/x - y = a and 1/x + y = b
21a + 21b = 5 ------------------------ (2)
On solving (1) * 21 & (2) * 28, we get
630a + 588b = 147
588a + 588b = 140
-----------------------------
42a = 7
a = 1/6.
Substitute a = 6 in (1), we get
30a + 28b = 7
30(1/6) + 28b = 7
5 + 28b = 7
28b = 7 - 5
28b =2
b = 2/28
b = 1/14.
We know that,
a = 1/x - y
1/6 = 1/x - y
x - y = 6 ----------- (3)
We know that,
b = 1/x + y
1/14 = 1/x + y
x + y = 14 ------------ (4).
On solving (3) & (4), we get
x + y = 14
x - y = 6
------------
2x = 20
x = 10
Substitute x = 10 in (4), we get
x + y = 14
10 + y = 14
y = 14 - 10
y = 4.
Therefore the speed of the boat in still water = 10km/hr.
Therefore the speed of the stream = 4km/hr