Tricks to solve Boats and Streams

Boat and Streams

Upstream: When the boat moves against the current of the river (i.e. in opposite direction), then the relative speed of the boat is the difference of the speed of the boat and stream. It is known as upstream speed.
Remember it with UP as going up the hill means against the direction of the force (speed) of the river.
If speed of boat or swimmer is x km/h and the speed of stream is y km/h then,

Speed of boat upstream = (x − y) km/h

Downstream: When the boat moves with the current of the river (i.e. in same direction), then the relative speed of the boat is the sum of the speed of the boat and stream. It is known as downstream speed.
Remember it with DOWN as going down the hill means towards the direction of the force (speed) of the river.
If speed of boat or swimmer is x km/h and the speed of stream is y km/h then,

Speed of boat downstream = (x + y) km/h

Important Points

When speed of boat is given then it means speed in the still water, unless it is stated otherwise.

Some Basic Formulas

Speed of boat in still water is
= ½ (Downstream Speed + Upstream Speed)

Speed of stream is
= ½ (Downstream Speed – Upstream Speed)

Types of Questions asked in Previous Exam By SSC

Type 1: When the distance covered by boat in downstream is same as the distance covered by boat upstream. The speed of boat in still water is x and speed of stream is y then ratio of time taken in going upstream and downstream is,
Short Trick:
Time taken in upstream : Time taken in Downstream = (x+y)/(x-y)
Example:
A man can row 9km/h in still water. It takes him twice as long as to row up as to row down. Find the rate of the stream of the river.
Solution:
Time taken in upstream : Time taken in Downstream = 2 : 1
Downstream speed : Upstream speed = 2 : 1
Let the speed of man = B, & speed of stream = S
B + S : B – S = 2/1
By using Componendo & Dividendo
B/R = 3/1, R = B/3
R = 9/3 = 3km/h
Type 2: A boat cover certain distance downstream in t₁ hours and returns the same distance upstream in t₂ hours. If the speed of stream is y km/h, then the speed of the boat in still water is:
Short Trick:
                Speed of Boat = y [(t₂ + t₁) / (t₂ – t₁)]
Example
A man can row certain distance downstream in 2 hours and returns the same distance upstream in 6 hours. If the speed of stream is 1.5 km/h, then the speed of man in still water is
Solution:
By using above formulae
= 1.5 [(6+2) / (6-2)] = 1.5 * (8/4) = 1.5 * 2 = 3km/h

Type 3: A boat’s speed in still water at x km/h. In a stream flowing at y km/h, if it takes it t hours to row to a place and come back, then the distance between two places is
Short Trick: Distance = [t*(x² – y²)]/2x
Example
A motor boat can move with the speed 7 km/h. If the river is flowing at 3 km/h, it takes him 14 hours for a round trip. Find the distance between two places?
Solution: By using above formulae
                = [14 * (7² – 3²)]/2* 7 = [14 * (49-9)]/2*7
= 14*40/2*7 = 40km

Type 4:  A boat’s speed in still water at x km/h. In a stream flowing at y km/h, if it takes t hours more in upstream than to go downstream for the same distance, then the distance is
Short Trick: Distance = [t*(x² – y²)]/2y
Example
A professional swimmer challenged himself to cross a small river and back. His speed in swimming pool is 3km/h. He calculated the speed of the river that day was 1km/h. If it took him 15 mins more to cover the distance upstream than downstream, then find the width of the river?
Solution: By using the above formulae
Distance = [t*(x² – y²)]/2y
= [(15/60) (3² – 1²)]/2*1
= [(1/4) * 8] / 2
= 2/2 = 1 km.

Type 5: A boat’s speed in still water at x km/h. In a stream flowing at y km/h, if it cover the same distance up and down the stream, then its average speed is
Short Trick: Average speed = upstream * downstream / man’s speed in still water
Note: The average speed is independent of the distance between the places.
Example
Find the average speed of a boat in a round trip between two places 18 km apart. If the speed of the boat in still water is 9km/h and the speed of the river is 3km/h?
Solution: Average speed = upstream * downstream / man’s speed in still water
Average speed = 6 * 12 / 9 = 8km/h

Question 1:

The speed of a boat in still water is 9 km/hr and the speed of the stream is 2.5 km/hr. How much time will the boat take to go 9.1 km against the stream?
(1) 1 hr. 20 min.
(2) 1 hr. 24 min.
(3) 1 hr. 30 min.
(4) 2 hrs. 24 min.

Solution: (2)

Speed of the boat against the stream

Time taken by the boat to go 9.1 km. against the stream

Question 2:

A boat travels upstream from P to Q and downstream from Q to P in 3 hours. If the speed of the boat in still water is 9 km/hr and the velocity of the stream is 3 km/hr, then what is the distance from P to Q?
(1) 14 km
(2) 8 km
(3) 12 km
(4) 6 km

Solution: (3)

Distance between P and Q
[Here, t = 3, u = 9 and v = 3]

Other Method :

Question 3:

A man can row 5 km/hr in still water and the velocity of the stream is 1.5 km/hr. He takes an hour when he travels upstream to a place and back again to the starting point. How far is the place from the starting point?
(1) 2.5 km
(2) 6.5 km
(3) 3.5 km
(4) 2.275 km

Solution: (4)

Let the distance of the place from the starting point be x km
The speed of the man along the stream = 5 + 1.5 = 6.5 km/hr and the speed of the man against the stream = 5 – 1.5 = 3.5 km/hr

Question 4:

A boat travels from P to Q along the stream and from Q to P against the stream in 3 hours. If the speed of the boat in still water is 4 km/hr, then what is the distance between P and Q?
(1) 8 km
(2) 6 km
(3) 12 km
(4) Data insufficient

Solution: (4)

Let the distance from P to Q be x km. and the velocity of the stream be y km./hr.

Since equation is one and two expressions (x and y) are unknown. Hence the data is inadequate.

Question 5:

A man can row

km/hr in still water and he finds that it takes him thrice as much time to row upstream as to row downstream (same distance). The speed of the current is
(1)