Boats and Streams
- 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 9km/hr and the speed of the current is 3 km/hr the distance between A and B is ?
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Speed downstream = (9 + 3) km/hr = 12km/hr
Speed upstream = = (9 - 3) km/hr = 6km/hr
Let the distance AB = d km
Then, d/6 + d/12 = 3Correct Option: D
Speed downstream = (9 + 3) km/hr = 12km/hr
Speed upstream = = (9 - 3) km/hr = 6km/hr
Let the distance AB = d km
Then, d/6 + d/12 = 3
⇒ 2d + d = 36
⇒ d = 12
∴ Distance AB = 12 km
- If the speed of a boat in still water is 20 km/hr and the speed of the current is 5 km/hr, then the time taken by the boat to travel 100 km with the current is :
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Here , speed of a boat in still water = 20 km/hr and the speed of the current = 5 km/hr
Distance = 100 km
Rate downstream of boat = (20 + 5) kmph = 25 kmphRequired time = Distance Rate downstream of boat
Correct Option: C
Here , speed of a boat in still water = 20 km/hr and the speed of the current = 5 km/hr
Distance = 100 km
Rate downstream of boat = (20 + 5) kmph = 25 kmphRequired time = Distance Rate downstream of boat Required time = 100 = 4 kmph 25
- A boat covers 12 km upstream and 18 km downstream in 3 hours, while it covers
. What is the speed of the current ?36 km upstream and 24 km downstream in 6 1 hrs 2
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Let the speed of boat in still water be p kmph and that of current be q kmph, then
According to question ,12 + 18 = 3........(i) p - q p + q 36 + 24 = 13 p - q p + q 2
By equation (i) × 3 – equation (ii),54 - 24 = 9 - 13 p + q p + q 2 ⇒ 30 = 5 ⇒ p + q = 12 .........(iii) p + q 2
From equation (i),⇒ 12 + 18 = 3 p - q 12
Correct Option: C
Let the speed of boat in still water be p kmph and that of current be q kmph, then
According to question ,12 + 18 = 3........(i) p - q p + q 36 + 24 = 13 p - q p + q 2
By equation (i) × 3 – equation (ii),54 - 24 = 9 - 13 p + q p + q 2 ⇒ 30 = 5 ⇒ p + q = 12 .........(iii) p + q 2
From equation (i),⇒ 12 + 18 = 3 p - q 12 ⇒ 12 = 3 - 3 = 3 p - q 2 2 ⇒ p - q = 12 × 2 = 8........(iii) 3 ∴ Speed of current = 1 (12 - 8) = 2 kmph 2
- A boat running downstream covers a distance of 30 km in 2 hours. While coming back the boat takes 6 hours to cover the same distance. If the speed of the current is half of that of the boat, then what is the speed of the boat in kmph?
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As per the given in above question ,
Downstream speed = 30/2 = 15 kmph
Upstream speed = 30/6 = 5 kmph
Let speed of the boat be p,
then speed of the current = p /2.p + p = 15 ........(i) 2 p - p = 5 ........(ii) 2
From either of the two equations, we can find the value of p, p = 10 kmph
Another set of formula which can serve as shortcut in above case isSpeed of the boat = Downstream Speed + Upstream Speed 2 Speed of the stream = Downstream Speed - Upstream Speed 2
Putting these in the above example,
Correct Option: C
As per the given in above question ,
Downstream speed = 30/2 = 15 kmph
Upstream speed = 30/6 = 5 kmph
Let speed of the boat be p,
then speed of the current = p /2.p + p = 15 ........(i) 2 p - p = 5 ........(ii) 2
From either of the two equations, we can find the value of p, p = 10 kmph
Another set of formula which can serve as shortcut in above case isSpeed of the boat = Downstream Speed + Upstream Speed 2 Speed of the stream = Downstream Speed - Upstream Speed 2
Putting these in the above example,Speed of the boat = 15 + 5 = 10 kmph 2 & Speed of the stream = 15 - 5 = 5 kmph 2
- A boat covers 20 km in 4 hours along the current and 9 km in 3 hours against the current. What is the speed of the current ?
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On the basis of given details in above question , we have
Rate downstream = 20 = 5 kmph 4 Rate upstream = 9 = 3 kmph 3 ∴ Speed of current = 1 (Rate downstream - Rate upstream) 2
Correct Option: B
On the basis of given details in above question , we have
Rate downstream = 20 = 5 kmph 4 Rate upstream = 9 = 3 kmph 3 ∴ Speed of current = 1 (Rate downstream - Rate upstream) 2 Speed of current = 1 (5 - 3) = 1 kmph 2
