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A motor boat can travel 30 km upstream and 28 km downstream in 7 hrs it can travel 21km upstream and return in 5 hrs find the speed of the boat in still water and the speed of the stream.?
Most Upvoted Answer
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.
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.
Community Answer
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.
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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A motor boat can travel 30 km upstream and 28 km downstream in 7 hrs it can travel 21km upstream and return in 5 hrs find the speed of the boat in still water and the speed of the stream.?
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A motor boat can travel 30 km upstream and 28 km downstream in 7 hrs it can travel 21km upstream and return in 5 hrs find the speed of the boat in still water and the speed of the stream.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A motor boat can travel 30 km upstream and 28 km downstream in 7 hrs it can travel 21km upstream and return in 5 hrs find the speed of the boat in still water and the speed of the stream.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A motor boat can travel 30 km upstream and 28 km downstream in 7 hrs it can travel 21km upstream and return in 5 hrs find the speed of the boat in still water and the speed of the stream.?.
A motor boat can travel 30 km upstream and 28 km downstream in 7 hrs it can travel 21km upstream and return in 5 hrs find the speed of the boat in still water and the speed of the stream.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A motor boat can travel 30 km upstream and 28 km downstream in 7 hrs it can travel 21km upstream and return in 5 hrs find the speed of the boat in still water and the speed of the stream.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A motor boat can travel 30 km upstream and 28 km downstream in 7 hrs it can travel 21km upstream and return in 5 hrs find the speed of the boat in still water and the speed of the stream.?.
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