This page contains information about How to solve Boats and Streams Problem Quickly.
If a boat is going downstream and if it is moving along the direction of the stream. Then the net speed of the boat in this scenario is known as downstream speed. And if a boat is moving in the direction opposite to the direction of the stream. Then the net speed of the boat in this scenario is known as upstream speed.This page contains information about How to solve Boats and Streams Problem Quickly.
1.A boat covers 900 meters in 300 seconds against the stream and returns downstream in 3 minutes. What is the speed of the boat in still water?
Options:
A. 4 m/s
B. 5 m/s
C. 1 m/s
D. 3 m/s
Solution:
Upstream speed = 900/300 = 3m/s
Downstream speed = 900/3 * 60 = 900/180 = 5m/s
Speed in still water = 1/2 (speed downstream + speed upstream)
= 1/2 (5 + 3)
= ½ (8)
= 4 m/s
Correct option: A
2. A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.
Options:
A. 2 hr
B. 3 hr
C. 4 hr
D. 5 hr
Solution:
Speed downstream
= (13 + 4) km/hr
= 17 km/hr
Time taken to travel 68 km downstream
= $\frac{68}{17}$ hours
= 4 hours
Distance covered in 4 minutes = 35 * 4/60 = 2.333 km/hr
Correct option: C
3. A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:
Options:
A. 8.5 km/hr
B. 9 km/hr
C. 10 km/hr
D. 12.5 km/hr
Solution:
Man's rate in still water
= (15 - 2.5) km/hr
= 12.5 km/hr.
Man's rate against the current
= (12.5 - 2.5) km/hr
= 10 km/hr.
Correct option: C
1. What is the speed of the stream, if the speed of the boat against the stream is 6 km/hr and the speed of a boat in still water is 10km/hr?
Options:
A. 4 km/hr
B. 2 km/hr
C. 10 km/hr
D. 5 km/hr
Solution:
Let the speed of stream = x
Speed of boat = 10 km/hr
We know that, Upstream speed = speed of boat – speed of stream
6 = 10 – x
x = 10 – 6
x = 4 km/hr
Correct option: A
2. A man can row a boat upto 30 km down a river in 3 hours with the stream and can return back in 5 hours. What is the speed of the stream?
Options:
A. 4 km/hr
B. 2 km/hr
C. 6 km/hr
D. 5 km/hr
Solution:
Speed Downstream= 30/3 = 10 km/hr
Speed Upstream = 30/5 = 6 km/h
Speed of the stream = 1/2* (10 – 6) = 2 km/hr
Correct option: B
3. A man sail a boat to a place which is 24 km far. He reaches that place and comes back in 7 hours. He finds that he can sail a boat 3 km downstream in the same time as 2 km upstream. Find out the rate of the stream?
Options:
A. 1.43 km/hr
B. 2 km/hr
C. 6 km/hr
D. 5 km/hr
Solution:
Suppose, He moves 3km downstream in x hours = 3/x km/hr
Speed Upstream = 2/x km/hr
24/(3/x) + 24/(2/x) = 7
8x + 12x = 7
x = 7/20
x = 0.35
So, Downstream Speed = 3/x = 3/ 0.35 = 8.57 km/hr
Upstream Speed = 2/0.35 = 5.71 km/hr
Rate of the stream = 1/2 (8.57 – 5.71) = 2.86/2 = 1.43 km/hr
Correct option: A
1. Rahul can sail a boat 3 quarters of kilometer upstream in 11(1/4) minutes and downstream in 7(1/2) minutes. Find out the speed of Rahul in still water?
Options:
A. 9 km/ hr
B. 5 km/ hr
C. 4 km/ hr
D. 3 km/ hr
Solution:
Three-quarters of a kilometer = 750 meter
11(1/4) minutes = 45/4 = 675 seconds
7(1/2) minutes = 15/2 = 450 seconds
Upstream speed = 750/675 = 10/9 m/sec
Downstream speed = 750/450 = 5/3 m/sec
Speed in still water = ½ (10/9 + 5/3) = 25/18m/sec
To convert it into km/hr, multiply 25/18 by 18/5
= 5 km/hr
Correct option: B
2. A man’s speed with the current is 20 km/hr and the speed of the current is 5 km/hr. What is the man’s speed against the current?
Options:
A. 20 km/hr
B. 15 km/ hr
C. 5 km/ hr
D. 10 km/ hr
Solution:
Man’s speed with the current = 20 km/hr
speed of the man + speed of the current = 20 km/hr
Hence, speed of the man = 20 – 5 = 15 km/hr
speed of the current is 5 km/hr
Man’s speed against the current = speed of the man – speed of the current
Man’s speed against the current = 15 – 5 = 10 km/hr
Correct option: D
3.If a man sails a boat at the rate of 5 km/hr in still water. His upstream rate is 3 km/hr, then find the man’s speed along the current?
Options:
A. 7 km/hr
B. 5 km/hr
C. 8 km/hr
D. 10 km/hr
Solution:
Let the speed along with the current = x km/hr
Therefore, (x+3)/2 = 5
x = 7km/hr
Correct option: A