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- Question
A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:
Options- A. 2 mph
- B. 2.5 mph
- C. 3 mph
- D. 4 mph
- Correct Answer
- 2 mph
Explanation
Let the speed of the stream x mph. Then,Speed downstream = (10 + x) mph,
Speed upstream = (10 - x) mph.
∴ 36 - 36 = 90 (10 - x) (10 + x) 60 ⟹ 72x x 60 = 90 (100 - x2)
⟹ x2 + 48x - 100 = 0
⟹ (x+ 50)(x - 2) = 0
⟹ x = 2 mph.
- 1. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
Options- A. 4
- B. 5
- C. 6
- D. 10 Discuss
- 2. A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?
Options- A. 4 km/hr
- B. 6 km/hr
- C. 8 km/hr
- D. Data inadequate Discuss
- 3. A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
Options- A. 2.4 km
- B. 2.5 km
- C. 3 km
- D. 3.6 km Discuss
- 4. 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 Discuss
- 5. A man can row three-quarters of a kilometre against the stream in 11¼ minutes and down the stream in 7½ minutes. The speed (in km/hr) of the man in still water is:
Options- A. 2
- B. 3
- C. 4
- D. 5 Discuss
- 6. A boat covers a certain distance downstream in 1 hour, while it comes back in 1½ hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?
Options- A. 12 kmph
- B. 13 kmph
- C. 14 kmph
- D. 15 kmph
- E. None of these Discuss
- 7. The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is:
Options- A. 1.2 km
- B. 1.8 km
- C. 2.4 km
- D. 3.6 km Discuss
- 8. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
Options- A. 40 minutes
- B. 1 hour
- C. 1 hr 15 min
- D. 1 hr 30 min Discuss
- 9. A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:
Options- A. 1 km/hr
- B. 1.5 km/hr
- C. 2 km/hr
- D. 2.5 km/hr Discuss
- 10. Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:
Options- A. 16 hours
- B. 18 hours
- C. 20 hours
- D. 24 hours Discuss
Boats and Streams problems
Search Results
Correct Answer: 5
Explanation:
Let the speed of the stream be x km/hr. Then,
Speed downstream = (15 + x) km/hr,
Speed upstream = (15 - x) km/hr.
| ∴ | 30 | + | 30 | = 4 | 1 |
| (15 + x) | (15 - x) | 2 |
| ⟹ | 900 | = | 9 |
| 225 - x2 | 2 |
⟹ 9x2 = 225
⟹ x2 = 25
⟹ x = 5 km/hr.
Correct Answer: 6 km/hr
Explanation:
| Rate downstream = | ❨ | 16 | ❩kmph = 8 kmph. |
| 2 |
| Rate upstream = | ❨ | 16 | ❩kmph = 4 kmph. |
| 4 |
| ∴ Speed in still water = | 1 | (8 + 4) kmph = 6 kmph. |
| 2 |
Correct Answer: 2.4 km
Explanation:
Speed downstream = (5 + 1) kmph = 6 kmph.
Speed upstream = (5 - 1) kmph = 4 kmph.
Let the required distance be x km.
| Then, | x | + | x | = 1 |
| 6 | 4 |
⟹ 2x + 3x = 12
⟹ 5x = 12
⟹ x = 2.4 km.
Correct Answer: 10 km/hr
Explanation:
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 Answer: 5
Explanation:
We can write three-quarters of a kilometre as 750 metres,
and 11¼ minutes as 675 seconds.
| Rate upstream = | ❨ | 750 | ❩m/sec | = | 10 | m/sec. |
| 675 | 9 |
| Rate downstream = | ❨ | 750 | ❩m/sec | = | 5 | m/sec. |
| 450 | 3 |
| ∴ Rate in still water = | 1 | ❨ | 10 | + | 5 | ❩m/sec |
| 2 | 9 | 3 |
| = | 25 | m/sec |
| 18 |
| = | ❨ | 25 | x | 18 | ❩km/hr |
| 18 | 5 |
= 5 km/hr.
Correct Answer: 15 kmph
Explanation:
Let the speed of the boat in still water be x kmph. Then,
Speed downstream = (x + 3) kmph,
Speed upstream = (x - 3) kmph.
| ∴ (x + 3) x 1 = (x - 3) x | 3 |
| 2 |
⟹ 2x + 6 = 3x - 9
⟹ x = 15 kmph.
Correct Answer: 3.6 km
Explanation:
Speed downstream = (15 + 3) kmph = 18 kmph.
| Distance travelled = | ❨ | 18 x | 12 | ❩km = 3.6 km. |
| 60 |
Correct Answer: 1 hr 15 min
Explanation:
| Rate downstream = | ❨ | 1 | x 60 | ❩km/hr = 6 km/hr. |
| 10 |
Rate upstream = 2 km/hr.
| Speed in still water = | 1 | (6 + 2) km/hr = 4 km/hr. |
| 2 |
| ∴ Required time = | ❨ | 5 | ❩hrs = 1 | 1 | hrs = 1 hr 15 min. |
| 4 | 4 |
Correct Answer: 1 km/hr
Explanation:
Suppose he move 4 km downstream in x hours. Then,
| Speed downstream = | ❨ | 4 | ❩ | km/hr. |
| x |
| Speed upstream = | ❨ | 3 | ❩ | km/hr. |
| x |
| ∴ | 48 | + | 48 | = 14 or x = | 1 | . |
| (4/x) | (3/x) | 2 |
So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.
| Rate of the stream = | 1 | (8 - 6) km/hr = 1 km/hr. |
| 2 |
Correct Answer: 24 hours
Explanation:
Speed upstream = 7.5 kmph.
Speed downstream = 10.5 kmph.
| ∴ Total time taken = | ❨ | 105 | + | 105 | ❩hours = 24 hours. |
| 7.5 | 10.5 |
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