## Boats and Streams Practice Problems – Set 2

Boats and Streams Practice Problems – Set 2
1. A boat covers a distance of 30 km downstream in 2 hours while it takes 6 hours to cover the same distance upstream. How much time the boat will take to cover 90 km in still water?
(a) 6 hrs
(b) 9 hrs
(c) 15 hrs
(d) 16 hrs
(e) 22 hrs
2. A man rows 20 km downstream and 16 km upstream taking 4 hours each time. What is the speed of current?
(a) 0.4 kmph
(b) 0.5 kmph
(c) 0.6 kmph
(d) 0.1 kmph
(e) 0.7 kmph
3. A boat takes 4hours for traveling downstream from point P to point Q and coming back to point P upstream. If the velocity of the stream is 2km ph and the speed of the boat in still water is 4kmph, what is the distance between P and Q?
(a) 9 km
(b) 7 km
(c) 5 km
(d) 6km
(e) 12 km
4. Two boats travelling at 5km/h and 10km/hr, head directly towards each other. They begin at a distance of 20 kms from each other. How far apart are they (in kms) one minute before they collide?
(a) 1/4
(b) 1/2
(c) 3/4
(d) 5/6
(e) None of the above
5. 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 boat and speed of the water current, respectively.
(a) 2 : 1
(b) 3 : 2
(c) 8 : 3
(d) Couldn’t be determined
(e) None of the above
6. A man can row 30 km upstream and 44 km downstream in 10 hrs. Also, he can row 40 km upstream and 55 km downstream in 13 hrs. Find the speed of the man in still water.
(a) 5 km/hr
(b) 8 km/hr
(c) 10 km/hr
(d) 12 km/hr
(e) 15 km/hr
7. In a stream running at 2 km/hr, a motorboat goes 10 km upstream and back again to the starting point in 55 minutes. Find the speed (km/hr) of the motorboat in still water.
(a) 17
(b) 20
(c) 22
(d) 25
(e) 28
8. A boat runs at 22 km per hour along the stream and 10 km per hour against the stream. Find the ratio of speed of the boat in still water to that of the speed of the stream.
(a) 2:3
(b) 8:3
(c) 5:3
(d) 7:3
(e) 8 : 5
9. A boat covers a certain distance in half an hour downstream with the speed of 20km/hr in still water and the speed of current is 4km/hr. Then the distance travelled by the boat is:
(a) 6km
(b) 7km
(c) 12km
(d) 4km
(e) 9km
10. A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(a) 8 kmph
(b) 6 kmph
(c) 4 kmph
(d) 2 kmph
(e) 10 kmph
Solutions:
1. B) Upstream speed = 5 km/hr
Downstream speed = 15 km/hr
Speed of boat in still water = (5 + 15)/2 = 10 km/hr
Required time = 90/10 = 9 hrs
2. B) Speed downstream = 20/4 = 5 kmph
Speed upstream = 16/4 = 4 kmph
Speed of current = 1/2 * (5-4) = 0.5 kmph
3. D) Time taken by boat to travel upstream and downstream = 4 hours
Velocity of the stream, ½ (a-b) = 2km/hr
a-b = 4km/hr ……………….( 1)
velocity of the boat in still water = ½ (a+b) = 4km/hr
a+b = 8 km/hr ………………(2)
1 +2 we get a = 6 km/hr ,b = 2km/hr
let the distance between A and B be x km
x / 2 + x / 6 = 4
3x + x / 6 = 4  4x = 24 so,x = 6
distance between P and Q = 6km
4. A) They will collide after 20/(5 + 10) hrs ie, 80 min
And in each minute they approach 15/60km = 1/4km
5. C) Let boats rate upstream be x and boats rate downstream be y
ATQ,
Distance covered in 528 min = Distance covered in 240 min
=> Distance covered in 8h 48 min = Distance covered in 4 hr
=> x × 8 4/5 = y × 4
=> 44x/5 = 4y => y = 11/5x
Therefore required ratio = [(y + x)/2] : [(y – x)/2]
= [(11x/5 + x)/2] : [(11x/5 – x)/2] = [16x/5 × 1/2] : (6x/5 × ½) = 8x/5 : 3x/5 = 8 : 3
6. B) Let upstream speed = x, downstream speed = y km/hr
Then, 30/x + 44/y = 10 and 40/x + 55/y = 13
Put 1/x = a, 1/y = b
Solve the equations.
A = 1/5, b = 1/11
So, x = 5, y = 11
Speed in still water = (5+11)/2 = 8
7. C) Distance = time * [B^2 – R^2] / 2*B
10 =55/60 * [B^2 – 2^2] / 2*B
8. B) Speed along the stream = speed downstream = a = 22 km/hr
And speed against the stream = speed upstream = b = 10 km/hr.
Now, the speed in still water = a + b / 2 km/hr = (22 + 10) / 2 = 16 km/hr.
And the speed of stream = a - b / 2 km/hr = (22 - 10) / 2 = 6 km/hr.
Required ratio = speed in still water : speed of stream = 16:6 = 8:3.
9. C) Given that the speed of a boat in still water is 20 km/hr and speed of the stream is 4 km/hr.
Then the speed downstream = (20 + 4) km/hr = 24 km/hr.
The distance travelled in half an hour = 24 x 1/2 = 12 km.
Hence the distance travelled by the boat is 12 km.
10. B) M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4