Boats and Streams
- The speed of a stream is 3 km/ hr. and the speed of a man in still water is 5 km/hr. The time taken by the man to swim 26 km downstream is :
-
View Hint View Answer Discuss in Forum
Given in question , Speed of a stream is 3 km/ hr and the speed of a man in still water = 5 km/hr
Time = Distance Rate downstream
Rate downstream = 5 + 3 = 8 kmph
Correct Option: B
Given in question , Speed of a stream is 3 km/ hr and the speed of a man in still water = 5 km/hr
Time = Distance Rate downstream
Rate downstream = 5 + 3 = 8 kmphTime = 26 = 13 = = 3 1 hours 8 4 4
- 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
-
View Hint View Answer Discuss in Forum
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
- 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
-
View Hint View Answer Discuss in Forum
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 sailor goes 12 km downstream in 48 minutes and returns in 1 hour 20 minutes. The speed of the sailor in still water is :
-
View Hint View Answer Discuss in Forum
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
- A man can row 15km/ hr downstream and 9 km/hr upstream. The speed of the boat in still water is
-
View Hint View Answer Discuss in Forum
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
