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A boat takes 4 hrs to travel certain distance in a river in down stream and it takes 6 hrs to travel the same distance in upstream. Then the time taken by the boat to travel the same distance in still water is a) 4.8hrs b)9.8 hrs c)24hrs d)10 hrs The given answer is 4.8 hrs. Can you explain and and solve the problem?
Most Upvoted Answer
A boat takes 4 hrs to travel certain distance in a river in down strea...
Let the speed of the boat be v km/hr, the length of the river be d km and the speed of the river w km/hr.
d/(v+w)=4
d/(v-w)=6
1/(v+w)=4/d
1/(v-w)=6/d
v+w=d/4
v-w=d/6
2v=5d/12
v=5d/24
Therefore,
time=distance/speed
=d/v
From v=5d/24
24v=5d
time=d/v=24/5=4.8hrs
d/(v+w)=4
d/(v-w)=6
1/(v+w)=4/d
1/(v-w)=6/d
v+w=d/4
v-w=d/6
2v=5d/12
v=5d/24
Therefore,
time=distance/speed
=d/v
From v=5d/24
24v=5d
time=d/v=24/5=4.8hrs
Community Answer
A boat takes 4 hrs to travel certain distance in a river in down strea...
Problem: A boat takes 4 hrs to travel a certain distance in a river in downstream and it takes 6 hrs to travel the same distance in upstream. Then the time taken by the boat to travel the same distance in still water is:
Solution:
Let the speed of the boat in still water be x km/hr and the speed of the current be y km/hr.
When the boat travels downstream, its speed is (x+y) km/hr and when it travels upstream, its speed is (x-y) km/hr.
Let the distance between the two points be d km.
When the boat travels downstream, it takes 4 hours to cover the distance.
Hence, d = (x+y) * 4 km ...(1)
Similarly, when the boat travels upstream, it takes 6 hours to cover the distance.
Hence, d = (x-y) * 6 km ...(2)
Solving equations (1) and (2), we get:
(x+y) * 4 = (x-y) * 6
4x + 4y = 6x - 6y
10y = 2x
y = x/5
Substituting the value of y in equation (1), we get:
d = (x + x/5) * 4
d = 9x/5 * 4
d = 36x/5 km
Therefore, the time taken by the boat to travel the same distance in still water is:
t = d/x
t = (36x/5) / x
t = 7.2 hours
Hence, the answer is (a) 4.8 hours (rounded off to one decimal place).
Solution:
Let the speed of the boat in still water be x km/hr and the speed of the current be y km/hr.
When the boat travels downstream, its speed is (x+y) km/hr and when it travels upstream, its speed is (x-y) km/hr.
Let the distance between the two points be d km.
When the boat travels downstream, it takes 4 hours to cover the distance.
Hence, d = (x+y) * 4 km ...(1)
Similarly, when the boat travels upstream, it takes 6 hours to cover the distance.
Hence, d = (x-y) * 6 km ...(2)
Solving equations (1) and (2), we get:
(x+y) * 4 = (x-y) * 6
4x + 4y = 6x - 6y
10y = 2x
y = x/5
Substituting the value of y in equation (1), we get:
d = (x + x/5) * 4
d = 9x/5 * 4
d = 36x/5 km
Therefore, the time taken by the boat to travel the same distance in still water is:
t = d/x
t = (36x/5) / x
t = 7.2 hours
Hence, the answer is (a) 4.8 hours (rounded off to one decimal place).
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A boat takes 4 hrs to travel certain distance in a river in down stream and it takes 6 hrs to travel the same distance in upstream. Then the time taken by the boat to travel the same distance in still water is a) 4.8hrs b)9.8 hrs c)24hrs d)10 hrs The given answer is 4.8 hrs. Can you explain and and solve the problem?
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A boat takes 4 hrs to travel certain distance in a river in down stream and it takes 6 hrs to travel the same distance in upstream. Then the time taken by the boat to travel the same distance in still water is a) 4.8hrs b)9.8 hrs c)24hrs d)10 hrs The given answer is 4.8 hrs. Can you explain and and solve the problem? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A boat takes 4 hrs to travel certain distance in a river in down stream and it takes 6 hrs to travel the same distance in upstream. Then the time taken by the boat to travel the same distance in still water is a) 4.8hrs b)9.8 hrs c)24hrs d)10 hrs The given answer is 4.8 hrs. Can you explain and and solve the problem? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boat takes 4 hrs to travel certain distance in a river in down stream and it takes 6 hrs to travel the same distance in upstream. Then the time taken by the boat to travel the same distance in still water is a) 4.8hrs b)9.8 hrs c)24hrs d)10 hrs The given answer is 4.8 hrs. Can you explain and and solve the problem?.
A boat takes 4 hrs to travel certain distance in a river in down stream and it takes 6 hrs to travel the same distance in upstream. Then the time taken by the boat to travel the same distance in still water is a) 4.8hrs b)9.8 hrs c)24hrs d)10 hrs The given answer is 4.8 hrs. Can you explain and and solve the problem? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A boat takes 4 hrs to travel certain distance in a river in down stream and it takes 6 hrs to travel the same distance in upstream. Then the time taken by the boat to travel the same distance in still water is a) 4.8hrs b)9.8 hrs c)24hrs d)10 hrs The given answer is 4.8 hrs. Can you explain and and solve the problem? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boat takes 4 hrs to travel certain distance in a river in down stream and it takes 6 hrs to travel the same distance in upstream. Then the time taken by the boat to travel the same distance in still water is a) 4.8hrs b)9.8 hrs c)24hrs d)10 hrs The given answer is 4.8 hrs. Can you explain and and solve the problem?.
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A boat takes 4 hrs to travel certain distance in a river in down stream and it takes 6 hrs to travel the same distance in upstream. Then the time taken by the boat to travel the same distance in still water is a) 4.8hrs b)9.8 hrs c)24hrs d)10 hrs The given answer is 4.8 hrs. Can you explain and and solve the problem?, a detailed solution for A boat takes 4 hrs to travel certain distance in a river in down stream and it takes 6 hrs to travel the same distance in upstream. Then the time taken by the boat to travel the same distance in still water is a) 4.8hrs b)9.8 hrs c)24hrs d)10 hrs The given answer is 4.8 hrs. Can you explain and and solve the problem? has been provided alongside types of A boat takes 4 hrs to travel certain distance in a river in down stream and it takes 6 hrs to travel the same distance in upstream. Then the time taken by the boat to travel the same distance in still water is a) 4.8hrs b)9.8 hrs c)24hrs d)10 hrs The given answer is 4.8 hrs. Can you explain and and solve the problem? theory, EduRev gives you an
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