Boats and Streams problems
- 1. A motorboat can travel at 10 km/h in still water. It travelled 91 km downstream in a river and then returned to the same place, talking altogether 20 h. The rate of flow of river is?
Options- A. 3 km/h
- B. 4 km/h
- C. 2 km/h
- D. 5 km/h Discuss
Correct Answer: 3 km/h
Explanation:
Given, speed of boat = 10 km/h
Let speed of flow of river = x km/h
? Upstream speed of boat = (10 - x) km/h
and downstream speed of boat = = (10 + x) km/h
According to question.
91/(10 - x) + 91/(10 + x) = 20
? 91(10 + x + 10 - x) / (10 - x) (10 + x) = 20
? 91(20) / 100 - x2 = 20
? 91 = 100 - x2
? x2 = 9
? x = 3
- 2. A boat has to travel upstream 20 km distance from point X of a river to points Y. The total time taken by boat in travelling from point X to Y and Y to X is 41 min 40 s. What is the speed of the boat?
Options- A. 66 km/h
- B. 72 km/h
- C. 48 km/h
- D. Cannot be determined Discuss
Correct Answer: Cannot be determined
Explanation:
Let x be the speed of the boat and y be the speed of the current.
Speed upstream = (x - y) km/h
Speed downstream = (x + y) km/h
According to the question,
20 /(x - y) + 20/(x + y) = 25/36
In this equation, there are two variables but only one equation. So, the value of x cannot be determined.
- 3. Speed of motorboat in still water is 45 km/h. If the motor travels 80 km along the stream in 1 h 20 min, then the time taken by it to cover the same distance against the stream will be?
Options- A. 4 h 20 min
- B. 3 h 40 min
- C. 2 h 40 min
- D. 2 h 55 min Discuss
Correct Answer: 2 h 40 min
Explanation:
Let speed of stream be x km/h
Given speed of motorboat in still water = 45 km/h
? Speed of boat along stream = (45 + x) km/h
According to the question,
45 + x = 80 x 11/3
? 45 + x = 80 x 3 / 4
? x = 60 - 45 = 15
? Speed of boat against stream = 45 - 15 = 30 km/h
Hence, required time = Distance / Speed = 80 / 30
= (8 x 60)/3 = 160 min
= 2 h 40 min
- 4. A boat's speed in still water is 5km/h. While river is flowing with a speed of 2km/h and time taken to cover a certain distance upstream is 2 h more than time taken to cover the same distance downstream. Find the distance?
Options- A. 10.5 km
- B. 11 km
- C. 10.9 km
- D. 15 km Discuss
Correct Answer: 10.5 km
Explanation:
Let the distance be D km.
Speed download = (5 +2) = 7 km/h
and speed upstream = (5 -2) = 3 km/h
According to the question,
D/3 - D/7 = 2
? 7D - 3D = 21 x 2
? D = (21 x 2)/4 = 10.5 km
- 5. A boat takes 9 h to travel a distance upstream and taken 3 h to travel the same distance downstream. If the speed of the boat in still water is 4 km/h, then what is the velocity of the stream?
Options- A. 4 km/h
- B. 3 km/h
- C. 6 km/h
- D. 2 km/h Discuss
Correct Answer: 2 km/h
Explanation:
Let velocity of the stream be x km/h
? Velocity of the boat downstream = (4 + x) km/h
and velocity of the boat upstream = (4 - x) km/h
According to the question, 3(4 + x) = 9(4 - x)
? 12 + 3x = 36 - 9x
? 12x = 24
? x = 2 km/h
- 6. A boat running upstream covers a distance of 10 km in 30 min and while running downstream, it covers the same distance in 25 min away and return, then the speed of the water current is?
Options- A. 2 km/h
- B. 3 km/h
- C. 1/2 km/h
- D. 1 km/h Discuss
Correct Answer: 1/2 km/h
Explanation:
Speed upstream = 10 / (30/60) = (10 x 60)/30 = 20 km/h
Speed downstream = 10/(25/60) = (10 x 60)/25 = 24 km/h
? Speed of the river's current = (24 - 20)/2 = 4/2 = 2 km/h
- 7. A steamer goes downstream from one port to another in 4 h. It covers the same distance upstream in 5 h. If the speed of the stream is 2 km/h, then find the distance between the two ports.?
Options- A. 50 km
- B. 60 km
- C. 70 km
- D. 80 km Discuss
Correct Answer: 80 km
Explanation:
Let the distance between the two ports be x km.
Then, speed downstream = x/4
And speed upstream = x/5
? Speed of the stream = [speed downstream + speed upstream] / 2 = (x/4 - x/5)/2
? (5x -4x)/40 = 2
? x/40 = 2
? x = 80 km
- 8. In a river, the ratio of the speed of stream and speed of a boat in still water is 2 : 5 Again, ratio of the speed of stream and speed of an another boat in still water is 3 : 4. What is the ratio of the speeds of the first boat to the second boat in still water?
Options- A. 10 : 7
- B. 15 : 8
- C. 4 : 3
- D. 5 : 4 Discuss
Correct Answer: 15 : 8
Explanation:
For the first boat,
Speed of stream : Speed of boat = 2: 5
Let speed of stream be 2x km/h and speed of boat = 5x km/h
Similarly, for the second boat
Speed of stream be 3y km/h and speed of boat = 4y
In both of the conditions, river is same.
? 2x = 3y
? x = 3y/2
Thus, required ratio in speeds of boats in still water
= Thus, required ratio in speeds of boats in still water
= 5x : 4y = (5 x 3)y/2 : 4y = 15 : 8
- 9. A man can row against the current three-fourth of a kilometre in 15 min and returns same distance in 10 min, then ratio of his speed to that of current is?
Options- A. 3 : 5
- B. 5 : 3
- C. 1 : 5
- D. 5 : 1 Discuss
Correct Answer: 5 : 1
Explanation:
Let the speed of man and current be U and V km/h, respectively.
Speed upstream = (U - V) km/h
Speed down stream = (U + V) km/h
According to the question,
(3 x 60)/(4 x 15) = U - V
? U - V = 3 ......(i)
and (3/4) x (60/10) = U + V
? U + V = 9/2 ...(ii)
On adding Eqs. (i) and (ii), we get
2U = 3 + 9/2
? U = 15/4
On putting the value of U in Eq. (ii), we get
15/4 + V = 9/2
V = 9/2 - 15/4 = 18 - 15/4
? V = 3/4
Hence, speed of man U = 15/4 and
Speed of current V = 3/4
Hence, required ratio = 15/4 : 3/4 = 5 : 1
- 10. A boat running upstream takes 528 min to cover a certain distance, while it takes 240 min to cover the same distance running downstream. What is the ratio between the speed of the water current, respectively?
Options- A. 2 : 1
- B. 3 : 2
- C. 8 : 3
- D. Couldn't be determined Discuss
Correct Answer: 8 : 3
Explanation:
Let boat's rate upstream be U and boat's rate downstream = V
According to the question.
Distance covered in 528 min = Distance covered in 240 min
? Distance covered in 8 h 48 min = Distance covered in 4 h
? U x 84/5 = V x 4
? (44 x U)/5 = 4V
? V = (11 x U)/5
? Required ratio = (V + U)/2 : (V - U)/2
? = (11U/5 + U)/2 : (11U/5 - U)/ 2
? = 16U/5 : 6U/5 = 8 : 3
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