A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of boat in still water and the speed of stream.
Answers
Step-by-step explanation:
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.
NOTE: Sorry, for making such a lengthy calculations.