Boats and Streams
- A person can row a distance of one km upstream in ten minutes and downstream in four minutes. What is the speed of the stream ?
-
View Hint View Answer Discuss in Forum
Suppose Speed in still water = p km/h
Speed of current = q km/h∴ p + q = 1 4 60
p + q = 15p - q = 1 10 60
p - q = 6Speed of current = 1 [(p + q) - (p - q)] 2
Correct Option: A
Suppose Speed in still water = p km/h
Speed of current = q km/h∴ p + q = 1 4 60
p + q = 15p - q = 1 10 60
p - q = 6Speed of current = 1 [(p + q) - (p - q)] 2 Speed of current = 1 (15 - 6) = 9 = 4.5 kmph 2 2
- A boat goes 20 km downstream in one hour and the same distance upstream in two 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 p kmph and the rate of stream be q kmph.
Distance = 20 km
∴ Downstream rate= (p + q) kmph and upstream rate = (p – q) kmph.Now, 20 = 1 p + q
⇒ p + q = 20 ......(i)and 20 = 2 p - q
⇒ p – q = 10 ...(ii)
From (i) and (ii) we have p = 15 kmph.
We can find the required answer with the help of given formula :
Here, y = 20, t1 = 1, t2 = 2Speed of Boat = y 
1 + 1 
2 t1 t2
Correct Option: A
Let the speed of boat in still water be p kmph and the rate of stream be q kmph.
Distance = 20 km
∴ Downstream rate= (p + q) kmph and upstream rate = (p – q) kmph.Now, 20 = 1 p + q
⇒ p + q = 20 ......(i)and 20 = 2 p - q
⇒ p – q = 10 ...(ii)
From (i) and (ii) we have p = 15 kmph.
We can find the required answer with the help of given formula :
Here, y = 20, t1 = 1, t2 = 2Speed of Boat = y 1 + 1 2 t1 t2 Speed of Boat = 20 1 + 1 2 1 2
Speed of Boat = 15 km/hr
-
Find his rowing speed in still water.A man rows 750 m in 675 seconds against the stream and returns in 7 1 minutes. 2
-
View Hint View Answer Discuss in Forum
Let the speed of man in still water be p kmph and rate of stream be q kmph
∴ Distance = 750 km = 3 km 1000 4
Time = 675 secondsTime = 675 = 11 1 minutes 60 4 ∴ p - q = 3 4 45 4 p - q = 3 = 1 km / min 45 15 and p + q = 3 4 15 2 p + q = 3 × 2 = 1 km/min 4 15 10 ∴ Speed in still water = 1 1 + 1 = 1 3 + 2 2 10 15 2 30 Speed in still water = 1 km/min 12 Speed in still water = 1 × 60 kmph = 5 kmph 12
Using the given formula :Here, p = 750m 15 min 2 p = 750 × 2 × 60 1000 15
p = 6 km/hrq = 750m 675 min
Correct Option: C
Let the speed of man in still water be p kmph and rate of stream be q kmph
∴ Distance = 750 km = 3 km 1000 4
Time = 675 secondsTime = 675 = 11 1 minutes 60 4 ∴ p - q = 3 4 45 4 p - q = 3 = 1 km / min 45 15 and p + q = 3 4 15 2 p + q = 3 × 2 = 1 km/min 4 15 10 ∴ Speed in still water = 1 1 + 1 = 1 3 + 2 2 10 15 2 30 Speed in still water = 1 km/min 12 Speed in still water = 1 × 60 kmph = 5 kmph 12
Using the given formula :Here, p = 750m 15 min 2 p = 750 × 2 × 60 1000 15
p = 6 km/hrq = 750m 675 min q = 750 × 3600 = 4hrs 1000 675 Speed of Boat = 1 (p + q) 2 Speed of Boat = 1 (6 + 4) = 5 km/hrs 2
- A boat goes 40 km upstream in 8 hours and 36 km downstream in 6 hours. The speed of the boat in still water is :
-
View Hint View Answer Discuss in Forum
Given that , Speed upstream = 40 = 5 kmph 5 Speed downstream = 36 = 6 kmph 6 ∴ Speed of boat in still water = Rate downstream + Rate upstream 2 Speed of boat in still water = 1 (5 + 6) = 5.5 km/hrs 2
We can find the required answer with the help of given formula :Here, p = 36 = 6 km/hrs 6 q = 40 = 5 km/hrs 8
Correct Option: B
Given that , Speed upstream = 40 = 5 kmph 5 Speed downstream = 36 = 6 kmph 6 ∴ Speed of boat in still water = Rate downstream + Rate upstream 2 Speed of boat in still water = 1 (5 + 6) = 5.5 km/hrs 2
We can find the required answer with the help of given formula :Here, p = 36 = 6 km/hrs 6 q = 40 = 5 km/hrs 8 Speed of Boat = 1 (p + q) 2 Speed of Boat = 1 (6 + 5) = 5.5 km/h 2
- A boat goes 12 km downstream and comes back to the starting point in 3 hours. If the speed of the current is 3 km/hr, then the speed (in km/hr) 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, then
12 + 12 = 3 y + 3 y - 3 ⇒ 12 y - 3 + y + 3 = 3 (y + 3)(y -3)
Correct Option: B
Let the speed of boat in still water be y kmph, then
12 + 12 = 3 y + 3 y - 3 ⇒ 12 y - 3 + y + 3 = 3 (y + 3)(y -3)
⇒ 4 × 2y = y² – 9
⇒ y² – 8y – 9 = 0
⇒ y² – 9y + y – 9 = 0
⇒ y (y – 9) + 1 (y – 9) = 0
⇒ (y – 9) (y + 1) = 0
⇒ y = 9 because y ≠ –1
∴ Speed can't be negetive.
Hence, speed of boat in still water = 9 kmph
