Solved Questions on Boats and Streams
1. A boat can travel 60 km downstream in 5 hours and can cover the same distance upstream in 10 hours. What is the speed of the boat in still water?
a) 9 km/h
b) 15 km/h
c) 12 km/h
d) 20 km/h
Answer: a) 9 km/h
Explanation: Let the speed of the boat be x km/h. The speed of the stream is given by the formula:
Speed of boat in still water = (Speed downstream + Speed upstream)/2.
So, (60/5 + 60/10)/2
= (12 + 6)/2
= 18/2
= 9 km/h.
Therefore, the speed of the boat in still water is 9 km/h.
2. A boat takes 4 hours to travel 24 km upstream and 3 hours to travel 36 km downstream. What is the speed of the stream?
a) 2 km/h
b) 3 km/h
c) 4 km/h
d) 5 km/h
Answer: b) 3 km/h
Explanation: Let the speed of the boat be x km/h. The speed of the stream is given by the formula:
Speed of stream = (Speed downstream - Speed upstream)/2.
So, (36/3 - 24/4)/2 = (12 - 6)/2 = 6/2 = 3 km/h.
Therefore, the speed of the stream is 3 km/h.
3. A boat travels 90 km downstream in 6 hours. What is the speed of the boat in still water if the speed of the stream is 5 km/h?
a) 5 km/h
b) 10 km/h
c) 15 km/h
d) 20 km/h
Answer: b) 10 km/h
Explanation: Let the speed of the boat be x km/h. The speed of the stream is given as 5 km/h. The speed downstream is (x + 5) km/h,
From the given information,
90 / (x + 5) = 6
Solving this equation, we get x = 10 km/h.
4. A boat covers a certain distance upstream in 5 hours, while it takes 3 hours to cover the same distance downstream. If the speed of the boat in still water is 12 km/h, what is the speed of the stream?
a) 12 km/h
b) 5 km/h
c) 3 km/h
d) 2 km/h
Answer: c) 3 km/h
Explanation: Let the speed of the stream be y km/h. The speed downstream is (12 + y) km/h, and the speed upstream is (12 - y) km/h.
From the given information, we can write two equations:
Distance / (12 + y) = 3 and Distance / (12 - y) = 5.
Dividing these equations, we get (12 - y) / (12 + y) = 3/5.
Solving this equation, we get y = 3 km/h.
5. A boat can travel at a speed of 14 km/h in still water. If the speed of the stream is 4 km/h, find the time taken by the boat to go 72 km downstream.
a) 5 hours
b) 4 hours
c) 3 hours
d) 2 hours
Answer: b) 4 hours.
Explanation: The boat's speed in still water is 14 km/h, and the speed of the stream is 4 km/h. When going downstream,
Effective speed downstream = Speed of boat in still water + Speed of stream
= 14 km/h + 4 km/h
= 18 km/h
Now, we can use the formula Time = Distance / Speed
Time is taken in downstream = 72 km / 18 km/h
= 4 hours
Worksheet on Boats and Streams
1. A boat travels downstream at a speed of 20 km/h and upstream at a speed of 15 km/h. If the distance of the upstream journey is 45 km and the downstream journey is 80 km, what is the total time taken for the round trip?
a) 5 hours
b) 6 hours
c) 7 hours
d) 8 hours
Answer: c) 7 hours.
2. If the speed of the stream is 5 km/h, and the boat can travel at a speed of 30 km/h in still water, what is the boat's speed when travelling downstream?
a) 35 km/h
b) 25 km/h
c) 30 km/h
d) 20 km/h
Answer: a) 35 km/h.
3. A boat travels downstream for 15 km in one hour. The return journey upstream takes two hours. What is the speed of the stream?
a) 1.5 km/h
b) 2.45 km/h
c) 3.75 km/h
d) 4.15 km/h
Answer: c) 3.75 km/h.
4. If a boat travels 60 km upstream in 6 hours, and the speed of the boat in still water is 15 km/h while the speed of the stream is 5 km/h, how much time will it take for the boat to travel the same distance downstream?
a) 1 hour
b) 3 hours
c) 5 hours
d) 7 hours
Answer: b) 3 hours.
5. A boat can travel 120 km downstream in 4 hours. If the speed of the stream is 15 km/h, what is the speed of the boat in still water?
a) 15 km/h
b) 22 km/h
c) 25 km/h
d) 30 km/h
Answer: a) 15 Km/h
6. A boat takes 8 hours to travel 96 km downstream and 12 hours to travel the same distance upstream. What is the speed of the stream?
a) 4 km/h
b) 3 km/h
c) 2 km/h
d) 1 km/h
Answer: c) 2 km/h
7. A boat takes 2 hours to travel 50 km downstream and 10 hours to travel the same distance upstream. What is the speed of the stream if the speed of the boat in still water is 15 km/h?
a) 5 km/h
b) 7 km/h
c) 8 km/h
d) 10 km/h
Answer: d) 10 km/h
8. A boat covers 72 km downstream in 3 hours. If the speed of the boat in still water is 18 km/h, what is the speed of the stream?
a) 2 km/h
b) 4 km/h
c) 6 km/h
d) 8 km/h
Answer: c) 6 km/h
9. A motorboat, whose speed is 15 km/h in still water goes 84 km downstream and comes back in a total of 4 hours. What is the speed of the stream (in km/h)?
a) 5 hours
b) 6 hours
c) 7 hours
d) 8 hours
Answer: b) 6 hours.
10. A man has a speed of 15 km/hr with the current, and the speed of the current is 2.5 km/hr. What is the man's speed against the current?
a) 10 km/h
b) 15 km/h
c) 20 km/h
d) 25 km/h
Answer: a) 10 km/h
