## Boats and Streams

#### Boats and Streams

1. The speed of boat upstream and speed of boat downstream are 7 km/h and 13 km/h, respectively. Then the speed of stream and the speed of boat in still water is ?
1. 10 km/h and 3 km/h
2. 15 km/h and 9 km/h
3. 20 km/h and 6 km/h
4. 40 km/h and 12 km/h

1. Rate in still water=[(1/2)(u+v)] km/h
Rate of current=[(1/2)(u-v)] km/h
where u= speed of boat in downstream
v=speed of boat in upstream

##### Correct Option: A

Rate in still water=[(1/2)(u+v)] km/h
Rate of current=[(1/2)(u-v)] km/h
where u= speed of boat in downstream
v=speed of boat in upstream

Speed of boat in still water=[(1/2)(7+13)] =10 km/h
Speed of the stream =[(1/2)(13-7)]=3 km/h

1. The speed of a boat in still water is 10 km/h. If it can travel 26 km downstream and 14 km upstream in the same time , then the speed of stream is ?
1. 2 km/h
2. 2.5 km/h
3. 3 km/h
4. None of these

1. Let the speed of the stream = x km/h
∴ Speed of boat in still water = 10 km/h
Speed of boat downstream = (x + 10) km/h
Speed of boat upstream=(10 - x) km/h

##### Correct Option: C

Let the speed of the stream = x km/h
∴Speed of boat in still water = 10 km/h
Speed of boat downstream = ( x + 10) km/h
Speed of boat upstream=(10 - x) km/h

∴ Time taken to travel 26 km downstream=[ 26 / ( 10 + x ) ] h
Time taken to travel 14 km upstream=[ 14 /( 10 - x )] h
⇒ By condition [ 26 / ( 10 + x)]=[ 14 / ( 10 - x)]
⇒ 26(10-x)=14(10+x)

⇒ 260-26x =140 + 14x
⇒ 40x=120
⇒ x = 3 Here, speed of stream = 3 km/h

1. A boat goes 40 km. upstream in 8 hours and 36 km. downstream in 6 hours. The speed of the boat in standing water is ?
1. 6.5 km.hr
2. 6 km/hr
3. 5.5 km/hr
4. 5 km/hr

1. Speed upstream = (40/8) km/hr = 5 km/hr
Speed downstream = (36/6) km/hr = 6 km/hr

Speed of boat in still water = (5 + 6)/2 km/hr = 5.5 km/hr.

##### Correct Option: C

Speed upstream = (40/8) km/hr = 5 km/hr
Speed downstream = (36/6) km/hr = 6 km/hr

Speed of boat in still water = (5 + 6)/2 km/hr = 5.5 km/hr.

1. If a man's rate with the current is 12 km/hr and the rate of the current is 1.5 km/hr then man's rate against the current is ?
1. 9 km/hr
2. 6.75 km/hr
3. 5.25 km/hr
4. 7.5 km/hr

1. Let the rate against the current be x km/hr.
Then, (12 - x) / 2 = 1.5

##### Correct Option: A

Let the rate against the current be x km/hr.
Then, (12 - x) / 2 = 1.5
⇒ 12 - x = 3
⇒ x = 9 km/hr

1. If a man rows at 5 km/hr in still water and 3.5 km/hr against the current his rate along the current is ?
1. 8.5 km/hr
2. 6.5 km/hr
3. 6 km/hr
4. 4.25 km/hr

1. Speed of current = 5 - 3.5 = 1.5 km/hr.

##### Correct Option: B

Speed of current = 5 - 3.5 = 1.5 km/hr.
So the speed of man along the current = 5 + 1.5 = 6.5 km/hr