Boats and Streams problems
- 1. 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 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Analyst, Bank Clerk, Bank PO
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.
- 2. A man went downstream for 28 km in a motor boat and immediately returned. It took the man twice as long to make the return trip. If the speed of the river flow were twice as high, the trip downstream and back would take 672 minutes. Find the speed of the boat in still water and the speed of the river flow.
Options- A. 12 km/hr, 3 km/hr
- B. 9 km/hr, 3 km/hr
- C. 8 km/hr, 2 km/hr
- D. 9 km/hr, 6 km/hr Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 9 km/hr, 3 km/hr
Explanation:
Let's call the speed of the boat in still water "b" and the speed of the river flow "r".
When the man goes downstream, he travels with the current, so his effective speed is b + r. When he goes upstream, he travels against the current, so his effective speed is b - r.
We know that the man traveled 28 km downstream and then immediately returned, so his total distance traveled is 56 km. We also know that it took him twice as long to make the return trip, so his time going upstream was twice his time going downstream.
Using the formula distance = rate x time, we can set up two equations:
28 = (b + r) * t1
28 = (b - r) * 2t1
where t1 is the time it took the man to go downstream.
Simplifying the second equation, we get:
14 = (b - r) * t1
Now let's consider what happens if the speed of the river flow is doubled. The new effective speed downstream would be b + 2r, and the new effective speed upstream would be b - 2r. The total distance traveled is still 56 km. We can set up two more equations:
56 = (b + 2r) * t2
56 = (b - 2r) * 2t2
where t2 is the new total time it takes to make the trip downstream and back.
Simplifying the second equation, we get:
28 = (b - 2r) * t2
Now we have four equations and four unknowns (b, r, t1, and t2). We can solve for them using substitution and elimination.
From the first equation, we can solve for t1:
t1 = 28 / (b + r)
From the second equation, we can solve for t1 in terms of t2:
t1 = 14 / (b - r)
Setting these two expressions for t1 equal to each other and simplifying, we get:
(b + r) / (b - r) = 2
Solving for r in terms of b, we get:
r = b / 3
Now we can substitute this expression for r into any of the four equations to solve for the other variables. Let's use the first equation:
28 = (b + r) * t1
28 = (4b/3) * t1
t1 = 21 / (2b)
Now we can use this expression for t1 to solve for t2 in terms of b:
t2 = 42 / (2b - 4r)
t2 = 42 / (2b - 4b/3)
t2 = 126 / b
Finally, we can use the third equation to solve for b:
56 = (b + 2r) * t2
56 = (4b/3 + 2b/3) * 126 / b
56 = 2 * 126
b = 9
So the speed of the boat in still water is 9 km/h, and the speed of the river flow is b/3 = 3 km/h.
- 3. The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is ?
Options- A. 8 kmph
- B. 6 kmph
- C. 7.5 kmph
- D. 5.5 kmph Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 6 kmph
Explanation:
Speed of the stream = 1
Motor boat speed in still water be = x kmph
Down Stream = x + 1 kmph
Up Stream = x - 1 kmph
[35/(x + 1)] + [35/(x - 1)] = 12
x = 6 kmph
- 4. A boy can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is ?
Options- A. 1.8 kmph
- B. 2 kmph
- C. 2.2 kmph
- D. 1.5 kmph Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 1.5 kmph
Explanation:
Speed of Boy is B = 4.5 kmph
Let the speed of the stream is S = x kmph
Then speed in Down Stream = 4.5 + x
speed in Up Stream = 4.5 - x
As the distance is same,
=> 4.5 + x = (4.5 - x)2
=> 4.5 + x = 9 -2x
3x = 4.5
x = 1.5 kmph
- 5. A man rows his boat 60 km downstream and 30 km upstream taking 3 hrs each time. Find the speed of the stream ?
Options- A. 5 kmph
- B. 10 kmph
- C. 15 kmph
- D. 45 kmph Also asked in: GATE, Bank Clerk
Correct Answer: 5 kmph
Explanation:
Speed of the boat downstream s=a/t= 60/3 = 20 kmph
Speed of the boat upstream s= d/t = 30/3= 10 kmph
Therefore, The speed of the stream = =5 kmph
- 6. A boatman can row 3 km against the stream in 20 minutes and return in 18 minutes. Find the rate of current ?
Options- A. 1/3 kmph
- B. 2/3 kmph
- C. 1/4 kmph
- D. 1/2 kmph Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 1/2 kmph
Explanation:
Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr.
Speed in downstream = 3 x 60/18 = 10 km/hr
Rate of current = (10-9)/2 = 1/2 km/hr.
- 7. A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man ?
Options- A. 4.58 kms
- B. 6.35 kms
- C. 5.76 kms
- D. 5.24 kms Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 5.76 kms
Explanation:
Speed in still water = 6 kmph
Stream speed = 1.2 kmph
Down stream = 7.2 kmph
Up Stream = 4.8 kmph
x/7.2 + x/4.8 = 1
x = 2.88
Total Distance = 2.88 x 2 = 5.76 kms
- 8. A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
Options- A. 7:4
- B. 11:4
- C. 4:7
- D. 8:3 Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 8:3
Explanation:
Let the speed of the boat upstream be p kmph and that of downstream be q kmph
Time for upstream = 8 hrs 48 min = hrs
Time for downstream = 4 hrs
Distance in both the cases is same.
=> p x = q x 4
=> 44p/5 = 4q
=> q = 11p/5
Now, the required ratio of Speed of boat : Speed of water current
=
=> (11p/5 + p)/2 : (11p/5 - p)/2
=> 8 : 3
- 9. A boat whose speed in still water is 9 kmph, goes 12 km downstream and comes back in 3 hrs. Find the speed of the stream?
Options- A. 1 kmph
- B. 3 kmph
- C. 5 kmph
- D. 4 kmph Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 3 kmph
Explanation:
Let the speed of the stream = x kmph
From the given data,
=> x = 3 kmph
Therefore, the speed of the stream = 3 kmph
- 10. A man can row 8 kmh in still water. If the river is running at 2 kmh, it takes 4 hrs more upstream than to go downstream for the same distance. Then the distance is given by
Options- A. 54 kms
- B. 32 kms
- C. 45 kms
- D. 60 kms Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 60 kms
Explanation:
Let the distance be d.
=> 2d = 120
=> d = 60 kms.
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