[Aptitude] Boats and Streams made-easy using our STD-Table Method

In Aptitude by Support Staff

  1. Case#1: Basics
  2. Case 2: Time same but Different distance covered in each case
  3. Case #3: unknown variables
  4. Previous Articles

I hope you’ve mastered the STD table method from earlier articles on Time and Work / Pipes and Cistern.
We can use that STD method even in boats and streams question as well.

But first some terminologies

Downstream
  • Boat is moving along with flow of river (B), so water stream (S) helps the boat to move faster.
  • It is same like “A and B work together”. So their speed will increase and we can do addition.
  • Hence Downstream speed = speed of Boat PLUS speed of stream (B+S)
Upstream
  • Boat is moving against the direction of river. It is same like “Pipe A can fill the tank in 2 hours while Pipe B can empty the tank in 1 hours”
  • In short they work against each other, hence final speed is decreases so we’ve to subtract. (B-S)
  • Upstream speed = Speed of Boat MINUS speed of stream (B-S)

Case#1: Basics
Question: A man can row Upstream @15kmph and downstream @21 kmph, what is the speed of water in river?
Now construct the usual STD table from the given data

B alone S alone Downstream (B+S) Upstream (B-S)
Speed ?? 21 15
Time
Distance

As we’ve seen in earlier Time and work problems, we can do addition and subtraction in the Speed cells directly.
B+S=21…..eq(1)
B-S=15……eq(2)
Add both equations
(B+S) PLUS (B-S) = 21 PLUS 15
2B=36
B=36/2
B=18 kmph
We already know that
B+S=21
SO IF B is 18 kmph then S = 21 minus 18 = 3 kmph.
Answer: Speed of water is 3 kmph.
[Alternatively: You can directly calculate speed of water by subtracting eq(1) from eq(2)]

Shortcut Method

Above “equations” only for showing you the concept.
Otherwise in the exam hall you can directly subtract column 4 from column 3, divide it by “2” you get speed of column 2.
then subtract column 2 from column 3 you get speed of column 1:See this Image

shortcut method

DONE! No lengthy calculation required. But mind it: In the STD table, We can do direct addition, subtraction only for the speed “cells” and not for time cells.
You can also verify the answer from the table.

B alone S alone Downstream (B+S) Upstream (B-S)
Speed 18 3 21 15
Time
Distance

From the first two columns B minus S= 18 minus 3 = 15.
In the last column, you can see that Upstream (B-S) = 15.
So yes answer is correct.
Anyways this was quite easy no brainer. Time to make things a bit complicated with next question
Case 2: Time same but Different distance covered in each case
Q. A Man rows the boat downstream for 60 km and Upstream 36 km, taking 4 hours each time. What is the speed of this boat?
Fill up the STD table

B alone S alone Downstream (B+S) Upstream (B-S)
Speed ??
Time 4 4
Distance 60 36

Apply the STD formula on third column
Speed x Time = Distance
Speed x 4= 60
Speed = 60/4
Downstream speed =15 kmph
Same way calculate for fourth column, you’ll get upstream speed = 36/4=9kmph
Update the table

B alone S alone Downstream (B+S) Upstream (B-S)
Speed ?? 15 9
Time 4 4
Distance 60 36

Shortcut method revisited

Compare this with first case. We know the speeds of upstream and downstream, we can use the shortcut method.
shortcut method for  que2

For those still uncomfortable with shortcut method, just do it manually
B+S=15 ; from column 4
B-S=9 from column 3
add both equations
(B+S) PLUS (B-S) = 15 PLUS 9
2B=24
B==24/2 =12 kmph
Answer. Speed of boat is 12 km per hour.

Verify the answer

So far we’ve calculated that
B+S=15 and
B=12.
Hence S=15 minus B=15 minus 12 =3kmph
Update the table

B alone S alone Downstream (B+S) Upstream (B-S)
Speed 12 3 15 9
Time 4 4
Distance 60 36

For the speed cells, Column 1 minus column 2 equals column 4. Hence answer is correct.

Case #3: unknown variables
A boat sails downstream from point A to B, which is 10 km away from A, and then returns to A. If actual speed of the boat in still water is 3kmph, and the total upstream and downstream journey takes 12 hours. What must be the actual speed of boat for the trip from A to B to take exactly 100 minutes.
Difficulty of a question doesn’t depend on the length of question paragraph. Above sum has no ‘dum’ in it, just like our PM.  This can be solved using the universal “STD” method.
Given in the problem:
Speed of boat in still water (B alone) =3kmph
Length of river =10km
We know that total time  taken for upstream+ downstream=12 hours.
Suppose upstream takes journey takes “t” hours, then downstream journey takes= (12-t) hours. Fill up the table

From A to B From B to A
B alone S alone Downstream (B+S) Upstream (B-S)
Speed 3 ?? 3+s 3-s
Time 12-t t
Distance 10 10

Apply the STD formula for both upstream and downstream columns
Speed x time = distance
(3+s)*(12-t)=10 →(t-12)=10/(3+s)…eq(1)
(3-s)*(t)=10→t=10/(3-s)…eq(2)
The total time taken in upstream + downstream journey
(12-t)+ t=12
Substitute the values of (12-t) and (t) with the things from eq 1 and 2

See this image for calculation
calculation of boat equations
Therefore
S2=9-5=4

MIND IT: Square Roots

S2=4 that doesn’t mean s=2 only.
Because square of (-2) =(-2)*(-2)=(+4)
When you take square root of 4, it can be (+2) or (-2)
But Since speed of water is a positive value, we’ll use  s=(+2). But keep this thing in mind especially for ‘data-sufficiency’ problems.
Update the table

From A to B From B to A
B alone S alone Downstream (B+S) Upstream (B-S)
Speed 3 2 3+2=5 3-2=1
Time 12-t t
Distance 10 10

We are not concerned with finding time in this question but still for practice :find Upstream time
Speed xtime = distance
1 x t =10
t = 10/1=10 hours.
Upstream time is 10 hours.
Similarly downstream time is 2 hours.  (apply STD or use 12-t, answer is 2 hours)
Coming to the ultimate question
What must be the actual speed of boat for the trip from A to B to take exactly 100 minutes.
Rephrase:
We want to go downstream for 10 kilometers. Speed of river is 2 kmph. We want to cover this distance in exactly 100 minutes, how fast should we run this boat?
Make a new column
Assume that new speed of boat should be (Bn)

From A to B From B to A Special case: A to B
B alone S alone Downstream (B+S) Upstream (B-S) Downstream (Bn+S)
Speed 3 2 5 1 (Bn+2)
Time 2 hrs 10 hrs 100 minutes
Distance 10 10 10

MIND IT: all units must be in same format

To get correct answers in STD formula, everything must be in same format.
Either “kilometer-hour format OR metre-second format”
Let’s stick to hours in this case.
Convert 100 minutes into hours
60 minutes =1 hour
1 minute =1/60 hour
Multiply both sides with 100
100 minutes = (100/60) hours.
(In short: When you want to convert minutes into hours, just divide minutes by 60)
Apply STD formula on last column

Speed  x time = distance
(Bn+2) x 100/60=10
(Bn+2) =60×10/100
(Bn+2) =6
Bn=6-2
Bn=4 kmph
Final answer: if we wish to cover 10 km downstream in 100 minutes, we must run the boat at the speed of 4kmph.
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