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In a certain time a boat can cover 168 km downstream and in the same time it can cover 96 km upstream. If the speed of boat in still water is 11 km/h, then find the speed of current.
- a)2.5 km/h
- b)3 km/h
- c)3.5 km/h
- d)4 km/h
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In a certain time a boat can cover 168 km downstream and in the same t...
Given:
In a certain time a boat can cover 168 km downstream and in the same time it can cover 96 km upstream.
Speed of boat in still water is 11 km/h.
Formula used:
Downstream speed = Speed of the boat in still water + Speed of the stream
Upstream speed = Speed of the boat in still water – Speed of the stream
Calculation:
Let the time taken by boat to cover 168 km downstream = ‘t’ hours
So, the time taken by boat to cover 96 km upstream = ‘t’ hours
The downstream speed of boat = (168/t) km/h
And the upstream speed of boat = (96/t) km/h
According to the question:
⇒ [(168/t) + (96/t)]/2 = 11
⇒ (168 + 96)/2t = 11
⇒ 264/2t = 11
⇒ t = 12 hours
∴the speed of current = [(168/12) - (96/12)]/2 = (14 - 8)/2 = 3 km/h
In a certain time a boat can cover 168 km downstream and in the same time it can cover 96 km upstream.
Speed of boat in still water is 11 km/h.
Formula used:
Downstream speed = Speed of the boat in still water + Speed of the stream
Upstream speed = Speed of the boat in still water – Speed of the stream
Calculation:
Let the time taken by boat to cover 168 km downstream = ‘t’ hours
So, the time taken by boat to cover 96 km upstream = ‘t’ hours
The downstream speed of boat = (168/t) km/h
And the upstream speed of boat = (96/t) km/h
According to the question:
⇒ [(168/t) + (96/t)]/2 = 11
⇒ (168 + 96)/2t = 11
⇒ 264/2t = 11
⇒ t = 12 hours
∴the speed of current = [(168/12) - (96/12)]/2 = (14 - 8)/2 = 3 km/h
Most Upvoted Answer
In a certain time a boat can cover 168 km downstream and in the same t...
Understanding the Problem:
Given that the boat can cover 168 km downstream and 96 km upstream in the same time. The speed of the boat in still water is 11 km/h.
Approach to Solution:
Let the speed of the current be x km/h.
Speed downstream:
Speed downstream = (speed of boat in still water) + (speed of current)
Speed downstream = 11 + x km/h
Speed upstream:
Speed upstream = (speed of boat in still water) - (speed of current)
Speed upstream = 11 - x km/h
Time taken downstream:
Time taken downstream = Distance / Speed
Time taken downstream = 168 / (11 + x) hours
Time taken upstream:
Time taken upstream = Distance / Speed
Time taken upstream = 96 / (11 - x) hours
Since the boat takes the same time to cover both distances:
168 / (11 + x) = 96 / (11 - x)
Solving the equation:
168(11 - x) = 96(11 + x)
1848 - 168x = 1056 + 96x
264x = 792
x = 792 / 264
x = 3 km/h
Therefore, the speed of the current is 3 km/h. Hence, option B is the correct answer.
Given that the boat can cover 168 km downstream and 96 km upstream in the same time. The speed of the boat in still water is 11 km/h.
Approach to Solution:
Let the speed of the current be x km/h.
Speed downstream:
Speed downstream = (speed of boat in still water) + (speed of current)
Speed downstream = 11 + x km/h
Speed upstream:
Speed upstream = (speed of boat in still water) - (speed of current)
Speed upstream = 11 - x km/h
Time taken downstream:
Time taken downstream = Distance / Speed
Time taken downstream = 168 / (11 + x) hours
Time taken upstream:
Time taken upstream = Distance / Speed
Time taken upstream = 96 / (11 - x) hours
Since the boat takes the same time to cover both distances:
168 / (11 + x) = 96 / (11 - x)
Solving the equation:
168(11 - x) = 96(11 + x)
1848 - 168x = 1056 + 96x
264x = 792
x = 792 / 264
x = 3 km/h
Therefore, the speed of the current is 3 km/h. Hence, option B is the correct answer.
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In a certain time a boat can cover 168 km downstream and in the same time it can cover 96 km upstream. If the speed of boat in still water is 11 km/h, then find the speed of current.a)2.5 km/hb)3 km/hc)3.5 km/hd)4 km/hCorrect answer is option 'B'. Can you explain this answer?
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