## Results

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### #1. A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.

Solution:

Speed downstream
= (13 4) km/hr
= 17 km/hr
Time taken to travel 68 km downstream= 68/17 hours
= 4 hours

### #2. 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:

Solution:

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.

### #3. 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?

Solution:

Let the man’s rate upstream be x kmph and that downstream be y kmph.
Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.

(x×44/5)=(y×4)
44/5x=4y
y=11/5x
Required ratio
=(y x/2):(yx/2)
=(16x/5×1/2):(6x/5×1/2)
=8/5:3/5
=8:3

### #4. 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:

Solution:

Let the speed of the stream be x km/hr
Then,
Speed downstream = (15 x) km/hr
Speed upstream = (15 – x) km/hr

30/(15 x) 30/(15x)=9/2
900/225x^2=9/2
9x^2=225
x^2=25
x=5km/hr

### #5. In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:

Solution:

Speed in still water
= 1/2 (11 5) kmph
= 8 kmph

### #6. 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?

Solution:

Rate downstream
16/2 kmph = 8 kmph
Rate upstream
= 16/4 kmph = 4 kmph
∴ Speed in still water
= 1/2 (8 4) kmph = 6 kmph

### #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:

Solution:

Speed downstream
= (15 3) kmph
= 18 kmph
Distance travelled
= (18×12/60) km
= 3.6 km

### #8. 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:

Solution:

Let the speed of the stream x mph.
Then,
Speed downstream = (10 x) mph
Speed upstream = (10 – x) mph

36/(10x)36/(10 x)=90/60
72x×60=90(100x^2)
x^2 48x100=0
(x 50)(x2)=0
x=2mph

### #9. 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?

Solution:

Speed downstream = (5 1) kmph = 6 kmph
Speed upstream = (5 – 1) kmph = 4 kmph
Let the required distance be x km
Then,

x/6 x/4 = 1

⇒ 2x 3x = 12
⇒ 5x = 12
⇒ x = 2.4 km