Boats and Streams: Solved Examples

Example 1. The speed of the boat in still water is 20 km/hr and the speed of the stream is 5 km/hr. Find the downstream speed and the upstream speed.
Sol : Here we have b = 20 km/hr and w = 5 km/hr
So the downstream speed = b + w = 20 + 5 = 25km/hr
The upstream speed = b – w = 20 - 5 = 15 km/hr
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Example 2. A man can row 10 km downstream in 15 minutes and the same distance upstream in 20 minutes. Find the speed of the boat in still water and the speed of the stream.
Sol : The distance covered by the man downstream in 15 minutes = 10 km, so the distance covered downstream in 60 minutes = 40km. Hence the downstream speed = d = 40 km/hr
The distance covered upstream in 20 minutes = 10 km, so the distance covered downstream in 60 minutes = 30 km. Hence the upstream speed = u = 30 km/hr.
The speed of the boat = (d+u)/2 = (40+30)/2 = 35km/hr
The speed of the stream = (d-u)/2 = (40-30)/2 =10/2 = 5km/hr
Example 3: A boat running downstream covers a distance of 24 km in 3 hours while for covering the same distance upstream, it takes 6 hours. What is the speed of the current?
Sol: The downstream speed = 24/3 = 8 km/hr
The upstream speed = 24/6 = 4 km/hr
The speed of the current = (8-4)/2 = 4/2 = 2km/hr
Example 4: Speed of the boat in still water is 15 km/hr and the speed of the current is 7 km/hr. Find the total time taken by a man rowing to a place at a distance of 88 km and back.
Sol: The downstream speed is 15 + 7 = 22 km/hr and the upstream speed = 15 - 7 = 8 km/hr.
The total time taken = (88/22) + (88/8) = 4+11 = 15hours.
Example 5: The speed of the boat in still water is 30 km/hr. It goes 75 km downstream and comes back in 9 hours. Find the speed of the current.
Sol: Let the speed of the current = 'x' km/hr
We have 75/(30+x) + 75/(30-x) = 9
⇒ 75(60/(900-x2)) = 9
⇒ 900-x2 = 500
⇒ x2 = 400
⇒ x = 20km/hr
Example 6: A boat takes 2.5 hours less to travel 100 km downstream than to travel 75 km upstream. If the speed of the current is 5 km/hr, find the speed of the boat in still water.
Sol: Let the speed of the boat is 'x' km/hr. We have
75/(x-5) - 100(x+5) = 5/2
⇒ 25(3(x+5) - 4(x-5) / x2 - 25) = 5/2
⇒ 10(3x+15 - 4x+20) = x2 - 25
⇒ 10(35 - x) = x2 - 25
⇒ 350 - 10x = x2 - 25
⇒ x2 + 25x - 15x - 375 = 0
⇒ x(x+25) - 15(x+25) = 0
⇒ (x+25) (x-15) = 0
⇒ x = 15 km/hr (Rejecting the negative value)
Example 7: A man can row 8 km/hr in still water. If the speed of the current is 2 km/hr and it takes 4 hours to a man to row a place and come back, then how far is the place?
Sol: The downstream speed = 8 + 2 = 10 km/hr and the upstream speed = 8 - 2 = 6 km/hr
Let the distance is 'x' km. We have
(x/10) + (x+6) = 4
⇒ x((3+5) / 30) = 4
⇒ x = (4*30) / 8 = 15km.
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Example 8: A boat running upstream takes 4 hours 24 minutes to cover a certain distance, while it takes 2 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water respectively?
Sol: Let x be the speed of boat and y be the speed of water ∴
⇒ 22/5(x-y) = 2(x+y)
⇒ 11x-11y = 5x+5y ⇒ 6x=16y ⇒ x/y = 8/3
Hence the ratio of the speed of the boat and speed of the water is 8: 3.