In this article, we shall understand how questions based on Boats and Streams can be solved, using the basic relation of speed, distance and time.
When the boat moves in the direction of the stream, it is called Downstream. When the boat moves in the opposite direction than that of the stream, it is called Upstream.
If the speed of a boat in still water is x km/h and the speed of the stream is y km/h, then
From this relationship, we can say that
Example 1) A man can row 6 km/h in still water and the river flows at 4km/h. If he takes 1.5 h to row to a place and back, how far is the place?
Solution- 2.5 km
Downstream speed = (6+4) km/h
Upstream speed = (6-4) km/h
Let distance be d, then
d/10 + d/2 = 3/2
10d = 30/2
Therefore d = 2.5 km
Example 2) Vinny can row 15km/h in still water and it takes twice as long to row up the stream than to row down. Find the rate of the stream.
Solution- 5km/h
The ratio between downstream and upstream speed = 2:1
Let the upstream speed be 2x, then the speed downstream will be x
Speed is still water = (v+u) / 2 = (2x + x) / 2 = 3x/2 = 15 (given)
Hence, x = 10 km/h
Speed of stream = (v-u)/2 = (20-10)/2 = 5 km/h
Example 3) The speed of the stream is 5 km/h. A motorboat goes 10 km upstream and back again to the starting point in 50 min. The speed of the motorboat in still water is?
Solution– 25km/h
Let the speed of the motorboat in still water be x km/h
Speed upstream = x-5 km/s
Speed downstream = x+5 km/h
Acc. to the question,
{10 / (x-5)} + {10 / (x+5)} = 50/60
20x * 6 = (x2 – 25) * 5
X2 – 24x – 25 = 0
x(x-25) + 1(x-25) = 0
(x+1) (x-25) = 0
X = 25, as x can not be negative.
Example 4) The speed of a boat is 36 km/h. It goes 56 km upstream in 1 hour 45 minutes. The time taken by it to cover the same distance down the stream will be?
Solution- 1 hour 24 mins
Speed upstream = (56*4)/7 = 32 km/h
Let the speed of the current = x km/h
Therefore 36-x = 32,
X = 4 km/h
Speed downstream = 36 + 4 = 40 km/h
Therefore time taken to cover 56 km at 40 km/hr = 56/40 = 7/5 h = 1 h 24 min
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