Boat and Stream Problems Tricks And Shortcuts With Examples

At the time of attempting an aptitude test,  you may have seen the questions from boat and stream. These are some of the topics in which your concepts should be clear in order to solve them quickly. In this article, we will see how to deal with this type of questions.

You should know this formula:

Speed = Distance/ Time

Basic Concepts of Boat and Stream Problems

Let’s see the basic concept of Boat and Stream problem.

Still Water: When no flow is visible in the water

• Speed of a boat in still water= (Upstream + downstream)/2

Stream: In this topic, it simply means the continuous flow of water

• Speed of a boat in stream= (downstream – Upstream )/2

The stream can be of two types

Downstream: Direction with the stream. [ When a boat is moving in the same direction as water flows]

• Speed= Speed of boat + Stream

Upstream: Direction opposite to stream. [ When a boat is moving in the opposite direction as water flows]

• Speed of Boat = Speed of boat – Stream

Types of Questions Asked from Boat and Stream Problems

• When Speed of the boat need to find first

  • Apply the formula considering the type of stream

Q. A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.

Boat’s speed = 13km/hr
Stream’s Speed = 4 km

Speed of boat = 13 km/hr + 4 km/hr
= 17 km/hr

Distance = 68 km

Time = Distance / speed
= 68/17
= 4 hours

• When Speed of the stream is missing

Q. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

speed of the motorboat = 15 km/hr
Speed of stream = x
Speed of motorboat in downstream = (15 + x)
Speed of motorboat in upstream = (15 – x)

Distance = 30 km
Total time taken = 9/2 hr ( converted time 4 hours 30 min in hours)

Time = Distance/Speed

Time required to go all the way in downstream = distance/ speed = 30 /(15+x)
Time required to come back all the way in upstreaam = distance/ speed = 30 /(15-x)

Downstream time + upstream time = total time
30/(15+x) +30/(15-x) = 9/2

((15 -x)*30 + 30(15+x))/(15+x)(15-x) = 9/2
(450 – 30x + 450 +30x)/ 225 -x2 = 9/2                                   [ (a+b)(a-b) =a²-b²)
900/225-x² = 9/2
1800 = 2025 – 9x² [ Since all are multiples of 9, dividing all by 9 to get standerd form)

200 = 225 = x²
x² = 225 – 200
x² = 25
x =5

• Finding Speed of a boat in still water

Q. In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is

Speed of boat in downstream = 11 km/hr
Speed of boat in upstream = 5 km /hr

Speed of a boat in still water (U + D ) /2

(11+5)/2 = 16/2 = 6 km/hr