Boats and Streams
- The current of a stream runs at the rate of 4 km an hour. A boat goes 6 km and comes back to the starting point in 2 hours. The speed of the boat in still water is
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Let the speed of boat in still water be y kmph.
According to question ,⇒ 6 + 6 = 2 y + 4 y - 4 ⇒ 6 
y - 4 + y + 4 
= 2 (y + 4)(y - 4)
⇒ 6y = y² – 16
⇒ y² – 6y – 16 = 0
Correct Option: B
Let the speed of boat in still water be y kmph.
According to question ,⇒ 6 + 6 = 2 y + 4 y - 4 ⇒ 6 y - 4 + y + 4 = 2 (y + 4)(y - 4)
⇒ 6y = y² – 16
⇒ y² – 6y – 16 = 0
⇒ y² – 8y + 2y – 16 = 0
⇒ y (y – 8) + 2 (y – 8) = 0
⇒ (y + 2) (y – 8) = 0
⇒ y = 8 kmph and y ≠ – 2 kmph
- A man can row 15km/ hr downstream and 9 km/hr upstream. The speed of the boat in still water is
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Given that , Rate downstream = 15 kmph
Rate upstream = 9 kmph
We know that ,Speed of boat in still water = 1 (Rate downstream + Rate upstream) = 1 (15 + 9) 2 2
Correct Option: D
Given that , Rate downstream = 15 kmph
Rate upstream = 9 kmph
We know that ,Speed of boat in still water = 1 (Rate downstream + Rate upstream) = 1 (15 + 9) 2 2 Speed of boat in still water = 1 × 24 = 12 kmph 2
- A sailor goes 12 km downstream in 48 minutes and returns in 1 hour 20 minutes. The speed of the sailor in still water is :
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Let the speed of sailor in still water be p kmph.
and Speed of current = q kmph∴ p + q = 12 48 60 p + q = 12 × 60 = 15 kmph ........( 1 ) 48 and, p - q = 12 80 60 p - q = 12 × 60 = 9 kmph ........( 2 ) 80
Adding equations ( 1 ) and ( 2 ) , 2p = 15 + 9 = 24
⇒ p = 12 kmph
Second method to solve this question :Here, p = 12 × 60 = 15 kmph 48 q = 12 4 3
q = 9 km/hr
Correct Option: A
Let the speed of sailor in still water be p kmph.
and Speed of current = q kmph∴ p + q = 12 48 60 p + q = 12 × 60 = 15 kmph ........( 1 ) 48 and, p - q = 12 80 60 p - q = 12 × 60 = 9 kmph ........( 2 ) 80
Adding equations ( 1 ) and ( 2 ) , 2p = 15 + 9 = 24
⇒ p = 12 kmph
Second method to solve this question :Here, p = 12 × 60 = 15 kmph 48 q = 12 4 3
q = 9 km/hrSpeed of Boat = 1 (p + q) 2
Speed of Boat = 1 (15 + 9) = 12 kmph 2
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rate of 5 km an hour. What is the speed of the boat in the still water?A boat moves downstream at the rate of 1 km in 7 1 minutes and upstream at the 2
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Rate downstream of boat = 1 kmph 15 2 × 60 Rate downstream of boat = 2 × 60 = 8 kmph 15
Rate upstream of boat = 5 kmph∴ Speed of boat in still water = 1 (Rate downstream + Rate upstream) 2 Speed of boat in still water = 1 (8 + 5) = 13 kmph 2 2 Speed of boat in still water = 6 1 kmph 2
We can find the required answer with the help of given formula :Here, p = 1km 15 min 2 p = 2 × 60 = 8 kmph 15
q = 5 km/hrSpeed of Boat = 1 (p + q) 2
Correct Option: B
Rate downstream of boat = 1 kmph 15 2 × 60 Rate downstream of boat = 2 × 60 = 8 kmph 15
Rate upstream of boat = 5 kmph∴ Speed of boat in still water = 1 (Rate downstream + Rate upstream) 2 Speed of boat in still water = 1 (8 + 5) = 13 kmph 2 2 Speed of boat in still water = 6 1 kmph 2
We can find the required answer with the help of given formula :Here, p = 1km 15 min 2 p = 2 × 60 = 8 kmph 15
q = 5 km/hrSpeed of Boat = 1 (p + q) 2 Speed of Boat = 1 (8 + 5) 2 Speed of Boat = 6 1 km/hr 2
- A man swims downstream a distance of 15 km in 1 hour. If the speed of the current is 5 km/ hour, the time taken by the man to swim the same distance upstream is
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Given , Distance travelled by man = 15 km
And speed of the current = 5 km/ hour
Let the speed of man in still water be y kmph.∴ 15 = 1 y + 5
⇒ y + 5 = 15 ⇒ y = 10 kmph
Correct Option: D
Given , Distance travelled by man = 15 km
And speed of the current = 5 km/ hour
Let the speed of man in still water be y kmph.∴ 15 = 1 y + 5
⇒ y + 5 = 15 ⇒ y = 10 kmph∴ Time taken in swimming upstream = 15 = 3 hours 10 - 5
