A motor boat can travel 30 km upstream and 28 km downstream in 7 hrs i...
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.
A motor boat can travel 30 km upstream and 28 km downstream in 7 hrs i...
Given:
Distance travelled upstream = 30 km
Distance travelled downstream = 28 km
Time taken for upstream and downstream journey = 7 hours
Distance travelled upstream and return = 21 km
Time taken for upstream and return journey = 5 hours
We need to find the speed of the boat in still water and the speed of the stream.
Let:
Speed of boat in still water = b km/hr
Speed of stream = s km/hr
Speed of boat upstream = (b - s) km/hr
Speed of boat downstream = (b + s) km/hr
Calculating speed of boat in still water:
Let's first consider the upstream and downstream journey of 30 km and 28 km respectively.
Using the formula: Time = Distance/Speed
Time taken to travel upstream = 30/(b-s)
Time taken to travel downstream = 28/(b+s)
As per the given information, the total time taken for upstream and downstream journey is 7 hrs.
Therefore, we can form the equation:
30/(b-s) + 28/(b+s) = 7
Simplifying the equation, we get:
15b/bs = 7
Similarly, for the upstream and return journey of 21 km, we can form the equation:
21/(b-s) + 21/(b+s) = 5
Simplifying the equation, we get:
21b/bs = 5
Dividing the above two equations, we get:
15/7 = b/2b
Therefore, b = 10.5 km/hr
Calculating speed of stream:
Using the formula: Time = Distance/Speed
For the upstream and downstream journey of 30 km and 28 km respectively, we can form the equation:
30/(10.5-s) + 28/(10.5+s) = 7
Simplifying the equation, we get:
s = 1.5 km/hr
Conclusion:
The speed of the boat in still water is 10.5 km/hr and the speed of the stream is 1.5 km/hr.
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