11/07/21 Answers

1. A man can row 8 km/hr in still water. In a river running at 2 km/hr an hour, it takes him 40 minutes to row to a place and back, how far off is the place?
Answer: 2.5 kms
Solution: u = 8 km/hr; v = 2 km/hr

Speed downstream = (u+v) = 10 km/hr; Speed upstream = (u-v) = 6 km/hr

Let x be the length of the river

x/10 + x/6 = 40/60; x = 2.5 kms

2. A man takes 3 hours 15 minutes to row a boat 13 kms downstream of a river and 1 hours 30 minutes to cover a distance of 4.5 kms upstream. Find the rate of current in km/hr.

 Answer: 1/2 km/hr
 Solution: Rate downstream = 13/(13/4) = 4 km/hr, Rate upstream = 4.5/3/2 = 3 km/hr; Rate of   current = 1/2(4-3) = 1/2 km/hr

3. Speed of a boat in standing water is 9 kmph and the speed of the stream is 1 kmph. A man rows to a place at a distance of 120 km and comes back to the starting point. The total time taken by him is:
Answer: 27 hours
Solution: Speed upstream = 9-1 = 8 kmph; Speed downstream = 9+1 =10 kmph. Total time taken = (120/8 + 120/10) = 27 hours.

4. A man can row upstream at 11 kmph and downstream at 15 kmph. What is the speed of rowing in still water and the rate of current.
Answer: 13 kmph and 2 kmph
Solution: Speed in still water = (11+15)/2 = 13 km/hr; Rate of current = (15-11)/2 = 2 km/hr

5. A boat can travel with a speed of 17 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 84 km downstream.
Answer: 4 hours
Solution: Speed downstream = (17+4)  = 21 km/hr. Time taken to travel 84 km downstream = 84/21 =  4 hours

6. A boat travels upstream from B to A and downstream from A to B in 3
hours. If the speed of the boat in still water is 9 km/hr and the speed of the current is 3 km/hr the distance between A and B is
Answer: 12 km
Solution: Let the distance be D. Downstream speed = 9+3 = 12 kmph Upstream speed = 9-3 = 6 kmph; D/12 + D/6 = 3, Solving D= 12 km.

7. A person swims downstream 64 km in 4 hours and 40 km upstream in 5 hours. Find his speed in still water and the speed of the stream.
Answer: 12 km/hr, 4 km/hr
Solution: Downstream speed = 64/4 = 16 kmph, Upstream speed = 40/5 = 8 kmph; Speed in still water = (16+8)/2 = 12 kmph, Speed of stream = (16-8)/2 = 4 kmph.

8. A boat covers a certain distance downstream in 5 hours but takes 8
hours to return upstream to the starting point. If the speed of the stream be 3 km/hr, what is the speed of boat in still water?
Answer: 13 km/hr.
Solution: Let the distance be D and the speed of boat in still water  be S. Downstream speed = S+3, Upstream speed = S-3 D/(S+3) = 5, D/(S-3) = 8; 5(S+3) = 8(S-3), Solving S=13 kmph

9. A man goes 5 kms against the current of the stream in 1 hour and goes 5.5 kms along the current in 30 minutes. How long will it take for him to go 4 kms in stationary water?
Answer: 30 minutes
Solution: Rate upstream = 5 km/hr, Rate downnstream = 5.5 * 60/30 = 11 km/hr; Speed in still water = (5+11)/2 = 8 km/hr, Time taken to travel 4 kms = 4/8 = 30 minutes.

10. The current of a stream runs at the rate of 4 km/hr. A boat goes 6 km and back to the starting point in 2 hours. The speed of the boat in still water is
Answer: 8 km/hr
Solution: Let the speed of boat in still water be x kmph, Given, 6/(x+4) + 6/(x-4) = 2; 12x = 2x^2 -32. x^2 -6x -16 = 0.
Solving x=8 or -2 As speed cannot be a (-) value, x=8 kmph

11. If the speed downstream is a km/hr and the speed upstream is b km/hr, then what is the difference between the speed of the boat in still water and rate of the stream?
Answer: b kmph
Solution: Difference = (a+b)/2 - (a-b)/2 = b kmph.

12. What is the speed of the boat in still water, if the boat covers a distance of 72 kms in 9 hours while running upstream and the same distance in 6 hours while running downstream?
Answer: 10 kmph
Solution: Speed Upstream = 72/9 = 8 kmph, Speed Downstream = 72/6 = 12 kmph;
Speed in still water = ( 8 + 12)/ 2 = 10 kmph

13. A fisherman can row a boat at 4 kmph in still water. If the velocity of current is 1.5 kmph and it takes him 1.5 hours for him to row to the other bank of the river and come back, find the distance between the two banks.
Answer: 2.58 km
Solution: Speed  downstream = 5.5 km, Speed upstream = 2.5 kmph;
 Distance = x km, x/5.5  + x/ 2.5  =  1.5, 8x = 1.5 * 5.5 * 2.5; x = 2.58 km ~

14. The speed of a boat in still water is 2 km/hr. If its speed upstream be 1 km/hr, then speed of the stream is
Answer: 1 km/hr
Solution: Speed of the boat upstream = Speed of boat in still water - Speed of stream 1 = 2 - Speed of stream Speed of stream = 1 kmph

15. A man can row with the stream at 11 km/hr and against the stream at 8 km/hr. The speed of the stream is
Answer: 1.5 km.hr
Solution: Speed of stream = 1/2 * (Downstream - Upstream) = (11-8)/2 = 1.5 kmph

16. A man can row 18 kmph in still water. It takes him twice as long to row up as to row down the river. Find the rate of stream.
Answer: 6 km/hr
Solution: Rate upstream = x kmph, Rate downstream = 2x kmph; Speed in still water = (2x+x)/2 = 18 kmph.
 x = 12 km/hr, Rate of the stream = (24-12)/2 = 6 km/hr.

17. The speed of a boat downstream is 15 km/hr and the speed of the stream is 1.5 km/hr. The speed of the boat upstream is
Answer: 12 km/hr
Solution: Speed of the boat downstream = Speed of boat in still water + Speed of stream 15 = Speed of boat in still water + 1.5 Speed of boat in still water = 13.5 kmph
Speed of the boat upstream = 13.5 - 1.5 = 12 kmph

18. A man can row downstream at 14 km/hr and upstream at 9 km/hr. Man's rate in still water is
Answer: 11.5 km/hr
Solution: Speed of man in still water = 1/2 * (Downstream Speed + Upstream Speed) = (14+9)/2 = 11.5 kmph

19. A man can row 8 kmph in still water. If the river is running at 2 kmph and it takes him 80 minutes to row to a place and come back, how far is this place?

Answer: 5 kms
Solution: Speed downstream = 10 km/hr Speed upstream = 6 km/hr. Let x be the distance to the place. x/10 + x/6 = 4/3 x = 5 kms

20. A boat covers 30 kms upstream and 50 kms downstream in 4 hours and it also covers 15 kms upstream and 37.5 kms in 2 hours 30 mins. Find the speed of the boat in still water.
Answer: 20 kmph
Solution: Let upstream and downstream speed be U and D. 30/U + 50/D = 4 and 15/U + 37.5/D = 2.5
Solving U=15 and D=25. Hence speed in still water = (U+D)/2 = 20 kmph