Boats and Streams problems
- 1. A motorboat travelling at the same speed, can cover 25 km upstream and 39 km downstream in 8 h. At the same speed, it can travel 35 km upstream and 52 km downstream in 11 h. The speed of the stream is?
Options- A. 2 km/h
- B. 3 km/h
- C. 4 km/h
- D. 5 km/h Discuss
Correct Answer: 4 km/h
Explanation:
Let the speed of a boat and stream be U and V km/h
? Speed of boat along stream = (U + V) km/h
and speed of boat against stream = (U - V) km/h
According to the question,
25/(U - V) + 39/(U + V) = 8 ....(i)
and 35/(U - V) + 52/(U + V ) = 11 ..(ii)
On multiplying Eq. (i) by 4 and Eq. (ii) by 3, then subtract Eq. (ii) from Eq, we get
100/(U - V) - 105/(U - V) = -1
? 5/(U - V) = 1
? U - V = 5 ...(iii)
On substituting the value of (U - V) = 5 in Eq. (i) we get
25/5 + 39/(U + V) = 8
? 39/(U + V) = 8 - 5
? U + V = 39/3
? U + V = 13 ....(iv)
On solving Eqs. (iii) and (iv), we get
U = 9 and V = 4
Hence, speed of stream = 4 km/h
- 2. The speed of a boat in still water is 4 km/hr and the speed of current is 2 km/hr. If the time taken to reach a certain distance upstream is 9 hours, find the time it will take to go same distance downstream?
Options- A. 2 hrs
- B. 2.5 hrs
- C. 3.5 hrs
- D. 3 hrs Discuss
Correct Answer: 3 hrs
Explanation:
Upstream distance = (4 - 2) x 9 = 18 km
? Required time = 18/(4 + 2) = 3 hrs.
- 3. Ramesh can row a certain distance downstream is 6 hours and return the same distance in 9 hours. If the speed of Ram, Ramesh in still water is 12 km/hr, find the speed of the stream.
Options- A. 2.4 km/hr
- B. 2 km/hr
- C. 3 km/hr
- D. Data inadequate Discuss
Correct Answer: 2.4 km/hr
Explanation:
? [(9 + 6)/(9 - 6)] x v = 12
? v = 2.4 km/hr
- 4. A man rows to a place 48 km distance and 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. Find the rate of the stream?
Options- A. 1 km/hr
- B. 2 km/hr
- C. 1.5 km/hr
- D. 2.5 km/hr Discuss
Correct Answer: 1 km/hr
Explanation:
Suppose that the man takes H hours to cover 4 km downstream and H house to cover 3 km upstream.
Then, 48H/4 + 48H/3 = 14
? H = 1/2
? Rate upstream = 3/(1/2)= 6 km/hr
and rate downstream = 4/(1/2) = 8 km/hr
? Rate of the stream = (8 - 6)/2 = 1 km/hr .
- 5. A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water:
Options- A. 1.8h
- B. 3h
- C. 4h
- D. 5h Discuss
Correct Answer: 3h
Explanation:
Upstream speed = B-S
Downstream speed = B+s
B-S = 15/5 = 3 km/h
Again B= 4S
Therefore B-S = 3= 3S
=> S = 1 and B= 4 km/h
Therefore B+S = 5km/h
Therefore, Time during downstream = 15/5 = 3h
- 6. A man can row 9 km/h in still water. It takes him twice as long as to row down. Find the rate of stream of the river?
Options- A. 3 1⁄3 Kmph
- B. 3 1⁄9Kmph
- C. 4 2⁄3 Kmph
- D. 4 1⁄3 Kmph Discuss
Correct Answer: 4 2⁄3 Kmph
Explanation:
Let man’s rate upstream be x km/hr. Then his rate downstream is 3 x km/hr Given: Speed in still water = 9 (1/3) = 28/3 km/hr i.e, ½ (a+b) = 28/3 km/hr ½ (x+3x) = 28/3 2x = 28/3 x = 28/ 2 x 3 = 14/3 km/hr rate upstream b = 14/3 km/hr and rate downstream a = 14/3 x 3 = 14 km/hr speed of the current = ½ (a-b) = ½ (14 – 14/3) = ½ (42-14/3) = 28/6 = 4 (2/3) km/hr
- 7. 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 Discuss
Correct Answer: 9 km/hr, 3 km/hr
Explanation:
Let the speed of the boat = p kmph
Let the speed of the river flow = q kmph
From the given data,
=> 56p - 56q -28p - 28q = 0
=> 28p = 84q
=> p = 3q.
Now, given that if
Hence, the speed of the boat = p kmph = 9 kmph and the speed of the river flow = q kmph = 3 kmph.
- 8. A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C which is at midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B ?
Options- A. 180 km
- B. 160 km
- C. 140 km
- D. 120 km Discuss
Correct Answer: 180 km
Explanation:
Speed in downstream = (14 + 4) km/hr = 18 km/hr;
Speed in upstream = (14 ? 4) km/hr = 10 km/hr.
Let the distance between A and B be x km. Then,
x/18 + (x/2)/10 = 19 ? x/18 + x/20 = 19 ? x = 180 km.
- 9. A motor boat takes 12 hours to go downstream and it takes 24 hours to return the same distance. what is the time taken by boat in still water?
Options- A. 15 h
- B. 16 h
- C. 8 h
- D. 20 h Discuss
Correct Answer: 16 h
Explanation:
If t1 and t2 are the upstream and down stream times. Then time taken in still water is given by
- 10. 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 Discuss
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
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