# Boats and Streams

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## Basic Concept with Examples

### FORMULAS:

Still water: If the speed of water of the river is zero, then water is said to be still.
Stream: If the water of the river is moving at a certain speed, then it is said to be a stream.
Speed of the boat: It means speed of the boat in still water.
Downstream: If the boat is moving in the direction of the stream.
Upstream: If the boat is moving against the direction of the stream.

If the speed of the boat in still water and stream be b and s km/hr
Downstream speed = (b + s) km/hr
Upstream speed = (b – s) km/hr
s = (Downstream speed + Upstream speed)/2
b = (Downstream speed – Upstream speed)/2

Q1) A boatman rows 1 km in 5 min along the stream and 6 km in 1 hour against the stream. The speed of the stream is?
1) 3 km/hr
2) 6 km/hr
3) 10 km/hr
4) 12 km/hr

Solution:

Let the speed of the boat in still water and stream be b and s km/hr
Speed of the boat along the stream be (b + s) km/hr = b + s = 12 km/hr
Speed of the boat against the stream be (b – s) km/hr = b – s = 6 km/hr
On solving, b = 9 km/hr, s = 3 km/hr
Hence, option 1.

Q2) A motorboat can travel at 10 km/hr in still water. It travelled 91 Km downstream in a river and then returned to the same place, taking altogether 20 hours. The rate of flow of the river is
1) 3 km/hr
2) 4 km/hr
3) 2 km/hr
4) 5 km/hr

Solution:

Speed of the boat = 10 km/hr
Let the speed of the stream be s km/hr
Upstream speed of the boat = (10 – s) km/hr
Downstream speed of the boat = (10 + s) km/hr
91/(10 - s) + 91/(10 + s) = 20
For the above equation to be true, 91 must be divisible by 10 – s and 10 + s. So, 10 – s = 7; 10 + s = 13
s = 3 km/hr
Hence, option 1.

Q3) A boat goes 48 Km downstream in 20 hours. It takes 4 hours more to cover the same distance against the stream. What is the speed of the boat in still water?
1) 2.2 km/hr
2) 2 km/hr
3) 4 km/hr
4) 4.2 km/hr

Solution:

Let the speed of the boat in still water and stream be b and s km/hr
Upstream speed of the boat = b – s = 48/24 = 2 km/hr
Downstream speed of the boat = b + s = 48/20 = 2.4 km/hr
b = 2.2 km/hr
Hence, option 1.

Q4) A sailor sails a distance of 48 Km along the flow of the river in 8 hours. If it takes 12 hours to return the same distance, then the speed of the flow of the river is
1) 0.5 km/hr
2) 1 km/hr
3) 1.5 km/hr
4) 2 km/hr

Solution:

Let the speed of the boat in still water and stream be b and s km/hr
Upstream speed of the boat = b – s = 48/12 = 4 km/hr
Downstream speed of the boat = b + s = 48/8 = 6 km/hr
s = 1 km/hr
Hence, option 2.

Q5) A boat takes 9 hours to travel a distance upstream and 3 hours to travel the same distance downstream. If the speed of the boat in still water is 4 km/hr, then the speed of the stream is
1) 2 km/hr
2) 3 km/hr
3) 4 km/hr
4) 6 km/hr

Solution:

Let the speed of the stream be s km/hr
Upstream speed of the boat = (4 – s) km/hr
Downstream speed of the boat = (4 + s) km/hr
According to the question, 3(4 + s) = 9(4 – s)
s = 2 km/hr
Hence, option 1.

Q6) A man can row at 10 km/hr in still water. It he takes total 5 hours to go to a place 24 km away and return, then the speed of the water current is
1) 2 km/hr
2) 3 km/hr
3) 0.5 km/hr
4) 1 km/hr

Solution:

Let the speed of the current/stream be s km/hr
Upstream speed = (10 – s) km/hr
Downstream speed = (10 + s) km/hr
24/(10 - s) + 24/(10 + s) = 5
For the above equation to be true, 24 must be divisible by 10 – s and 10 + s. So, 10 – s = 8; 10 + s = 12
Hence, s = 2 km/hr
Hence, option 1.

Q7) A steamer goes downstream from one port to another in 4 hours. It covers the same distance upstream in 5 hours. If the speed of the stream is 2 km/hr, then find the distance between the two ports.
1) 50 km
2) 60 km
3) 70 km
4) 80 km

Solution:

Let the distance between the two ports be x km.
Upstream speed = x/5 km/hr
Downstream speed = x/4 km/hr
Speed of the stream = (x/4 – x/5)/2 = 2
On solving, x = 80 km
Hence, option 4.
Q8) A motorboat travelling at some speed, can cover 25 km upstream and 39 km downstream in 8 hours. At the same speed, it can travel 35 km upstream and 52 km downstream in 11 hours. The speed of the stream is.
1) 2 km/hr
2) 3 km/hr
3) 4 km/hr
4) 5 km/hr

Solution:

Let the speed of the boat in still water and stream be b and s km/hr
Upstream speed = (b – s) km/hr
Downstream speed = (b + s) km/hr
25/(b - s) + 39/(b + s) = 8
35/(b - s) + 52/(b + s) = 11
For the above equations to be true, 25 and 35 must be divisible by b – s; 39 and 52 must be divisible by b + s.
So, b – s = HCF(25, 35) = 5; b + s = HCF(39, 52) = 13
s = 4 km/hr.
Hence, option 3.