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A boat P travels 40 km upstream from point A to point B in 10 hours and downstream from point B to point A in 5 hours. Another boat Q can travel from point A to a point C 30 km upstream in 5 hours.
What is the speed of the boat Q in still water?
- a)6 km/hr
- b)8 km/hr
- c)10 km/hr
- d)12 km/hr
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A boat P travels 40 km upstream from point A to point B in 10 hours an...
Given Data:
Boat P travels 40 km upstream from point A to point B in 10 hours and downstream from point B to point A in 5 hours.
Another boat Q can travel from point A to a point C 30 km upstream in 5 hours.
To find: The speed of the boat Q in still water.
Solution:
Let us assume the speed of boat P in still water as x km/hr and the speed of the current as y km/hr.
1. Calculation of speed of Boat P in still water
Using the formula,
Speed = Distance/Time
Speed of boat P upstream = (40 km)/(10 hours) = 4 km/hr
Speed of boat P downstream = (40 km)/(5 hours) = 8 km/hr
Now,
Speed of boat P in still water = (Speed of boat P upstream + Speed of boat P downstream)/2
= (4 km/hr + 8 km/hr)/2
= 6 km/hr
Therefore, the speed of boat P in still water is 6 km/hr.
2. Calculation of speed of current
Using the formula,
Speed of current = (Speed of boat P downstream - Speed of boat P in still water)/2
= (8 km/hr - 6 km/hr)/2
= 1 km/hr
Therefore, the speed of the current is 1 km/hr.
3. Calculation of speed of boat Q in still water
Let us assume the speed of boat Q in still water as z km/hr.
Using the formula,
Speed of boat Q upstream = (Speed of boat Q in still water) - (Speed of current)
5 = (z - 1)
z = 6 km/hr
Therefore, the speed of the boat Q in still water is 6 km/hr, which is given by option B.
Boat P travels 40 km upstream from point A to point B in 10 hours and downstream from point B to point A in 5 hours.
Another boat Q can travel from point A to a point C 30 km upstream in 5 hours.
To find: The speed of the boat Q in still water.
Solution:
Let us assume the speed of boat P in still water as x km/hr and the speed of the current as y km/hr.
1. Calculation of speed of Boat P in still water
Using the formula,
Speed = Distance/Time
Speed of boat P upstream = (40 km)/(10 hours) = 4 km/hr
Speed of boat P downstream = (40 km)/(5 hours) = 8 km/hr
Now,
Speed of boat P in still water = (Speed of boat P upstream + Speed of boat P downstream)/2
= (4 km/hr + 8 km/hr)/2
= 6 km/hr
Therefore, the speed of boat P in still water is 6 km/hr.
2. Calculation of speed of current
Using the formula,
Speed of current = (Speed of boat P downstream - Speed of boat P in still water)/2
= (8 km/hr - 6 km/hr)/2
= 1 km/hr
Therefore, the speed of the current is 1 km/hr.
3. Calculation of speed of boat Q in still water
Let us assume the speed of boat Q in still water as z km/hr.
Using the formula,
Speed of boat Q upstream = (Speed of boat Q in still water) - (Speed of current)
5 = (z - 1)
z = 6 km/hr
Therefore, the speed of the boat Q in still water is 6 km/hr, which is given by option B.
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Community Answer
A boat P travels 40 km upstream from point A to point B in 10 hours an...
Let P km/hr be the speed of boat P, and Q km/hr be the speed of boat Q.
Let s km/hr be the rate of flow of stream.
We have,
P - s = 40/10 = 4 and P + s = 40/5 = 8
Solving, we get P = 6 and s = 2
Again, Q - s = 30/5 = 6
Thus, s = 2 and Q = 8.
Thus, speed of boat Q in still water is 8 km/hr.
Hence, answer option (B) is correct.
Let s km/hr be the rate of flow of stream.
We have,
P - s = 40/10 = 4 and P + s = 40/5 = 8
Solving, we get P = 6 and s = 2
Again, Q - s = 30/5 = 6
Thus, s = 2 and Q = 8.
Thus, speed of boat Q in still water is 8 km/hr.
Hence, answer option (B) is correct.
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A boat P travels 40 km upstream from point A to point B in 10 hours and downstream from point B to point A in 5 hours. Another boat Q can travel from point A to a point C 30 km upstream in 5 hours.What is the speed of the boat Q in still water?a)6 km/hrb)8 km/hrc)10 km/hrd)12 km/hrCorrect answer is option 'B'. Can you explain this answer?
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