Boats and Streams Basics
This quiz follows Lesson 7: Boats and Streams — Upstream and Downstream from the course Time, Speed & Distance: Core Concepts for Competitive Exams.
In this lesson you learned how a flowing stream changes a boat’s effective speed. The key relationships are:
- Downstream speed = boat speed in still water + stream speed
- Upstream speed = boat speed in still water − stream speed
- Boat speed in still water = ##\dfrac{\text{downstream} + \text{upstream}}{2}##
- Stream speed = ##\dfrac{\text{downstream} – \text{upstream}}{2}##
Work through each question carefully, apply the correct formula, and check the explanation after every answer. All the best!
Q1. If the speed of a boat in still water is ##b## and the speed of the stream is ##s##, which expression gives the downstream speed?
When the boat moves with the stream, the stream helps it, so the downstream speed is the sum of the boat's still-water speed and the stream speed: ##b + s##.
Q2. A boat's speed in still water is ##12## km/h and the stream flows at ##3## km/h. What is the downstream speed?
Downstream ##speed = boat## speed + stream ##speed = 12 + 3 = 15## km/h.
Q3. A boat's speed in still water is ##12## km/h and the stream flows at ##3## km/h. What is the upstream speed?
Upstream ##speed = boat## speed − stream ##speed = 12 - 3 = 9## km/h.
Q4. The downstream speed of a boat is ##18## km/h and the upstream speed is ##10## km/h. What is the speed of the boat in still water?
Boat speed in still ##water = \dfrac{\text{downstream} + \text{upstream}}{2} = \dfrac{18 + 10}{2} = 14## km/h.
Q5. The downstream speed of a boat is ##18## km/h and the upstream speed is ##10## km/h. What is the speed of the stream?
Stream ##speed = \dfrac{\text{downstream} - \text{upstream}}{2} = \dfrac{18 - 10}{2} = 4## km/h.
Q6. A boat travels ##24## km downstream in ##2## hours. What is its downstream speed?
Downstream ##speed = \dfrac{\text{distance}}{\text{time}} = \dfrac{24}{2} = 12## km/h.
Q7. A boat covers ##30## km upstream in ##3## hours. What is its upstream speed?
Upstream ##speed = \dfrac{\text{distance}}{\text{time}} = \dfrac{30}{3} = 10## km/h.
Q8. A boat's speed in still water is ##10## km/h and the stream speed is ##2## km/h. How long does it take to travel ##24## km downstream?
Downstream ##speed = 10 + 2 = 12## km/h. ##Time = \dfrac{24}{12} = 2## hours.
Q9. A boat's speed in still water is ##10## km/h and the stream speed is ##2## km/h. How long does it take to travel ##24## km upstream?
Upstream ##speed = 10 - 2 = 8## km/h. ##Time = \dfrac{24}{8} = 3## hours.
Q10. The speed of a boat downstream is ##20## km/h and the speed of the stream is ##4## km/h. What is the boat's speed in still water?
Downstream ##speed = boat## speed + stream speed, so boat ##speed = 20 - 4 = 16## km/h.
Q11. The speed of a boat upstream is ##8## km/h and the speed of the stream is ##3## km/h. What is the boat's speed in still water?
Upstream ##speed = boat## speed − stream speed, so boat ##speed = 8 + 3 = 11## km/h.
Q12. A boat's speed in still water is ##15## km/h. It goes ##40## km downstream and returns the same distance upstream, taking ##6## hours in total. What is the speed of the stream?
Let stream speed be ##s##. Then ##\dfrac{40}{15+s} + \dfrac{40}{15-s} = 6##. Solving gives ##s = 5## km/h.
Q13. If the downstream speed is ##16## km/h and the upstream speed is ##8## km/h, what is the ratio of the boat's still-water speed to the stream speed?
Boat ##speed = \dfrac{16+8}{2} = 12## km/h and stream ##speed = \dfrac{16-8}{2} = 4## km/h. ##Ratio = 12 : 4 = 3 : 1##.
Q14. A boat covers a certain distance downstream in ##2## hours and the same distance upstream in ##4## hours. If the stream speed is ##3## km/h, what is the boat's speed in still water?
Let boat speed be ##b##. Then ##2(b+3) = 4(b-3)##, giving ##2b + 6 = 4b - 12##, so ##b = 9## km/h.
Q15. A boat's speed in still water is ##8## km/h and the stream speed is ##2## km/h. What is the total time to go ##30## km downstream and return ##30## km upstream?
Downstream ##time = \dfrac{30}{10} = 3## h; upstream ##time = \dfrac{30}{6} = 5## h. ##Total = 8## hours.
Q16. If the speed of a boat in still water is ##b## and the stream speed is ##s##, which expression gives the upstream speed?
Against the stream, the current opposes the boat, so upstream ##speed = b - s##.
Q17. A boat's downstream speed is ##22## km/h and its upstream speed is ##14## km/h. What is the speed of the stream?
Stream ##speed = \dfrac{\text{downstream} - \text{upstream}}{2} = \dfrac{22 - 14}{2} = 4## km/h.
Q18. A boat's downstream speed is ##22## km/h and its upstream speed is ##14## km/h. What is the boat's speed in still water?
Boat ##speed = \dfrac{\text{downstream} + \text{upstream}}{2} = \dfrac{22 + 14}{2} = 18## km/h.
Q19. A boat travels ##36## km downstream in ##3## hours. If the stream speed is ##2## km/h, what is the boat's speed in still water?
Downstream ##speed = \dfrac{36}{3} = 12## km/h. Boat ##speed = 12 - 2 = 10## km/h.
Q20. A boat's speed in still water is ##6## km/h and the stream speed is ##2## km/h. What is the ratio of its downstream speed to its upstream speed?
##Downstream = 6 + 2 = 8## km/h; ##upstream = 6 - 2 = 4## km/h. ##Ratio = 8 : 4 = 2 : 1##.