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

Upstream 

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 (BS)  
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)
BS=15……eq(2)
Add both equations
(B+S) PLUS (BS) = 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
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 (BS)  
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 (BS) = 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 (BS)  
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 (BS)  
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.
For those still uncomfortable with shortcut method, just do it manually
B+S=15 ; from column 4
BS=9 from column 3
add both equations
(B+S) PLUS (BS) = 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 (BS)  
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= (12t) hours. Fill up the table
From A to B  From B to A  
B alone  S alone  Downstream (B+S)  Upstream (BS)  
Speed  3  ??  3+s  3s 
Time  12t  t  
Distance  10  10 
Apply the STD formula for both upstream and downstream columns
Speed x time = distance
(3+s)*(12t)=10 →(t12)=10/(3+s)…eq(1)
(3s)*(t)=10→t=10/(3s)…eq(2)
The total time taken in upstream + downstream journey
(12t)+ t=12
Substitute the values of (12t) and (t) with the things from eq 1 and 2
See this image for calculation
Therefore
S^{2}=95=4
MIND IT: Square Roots
S^{2}=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 ‘datasufficiency’ problems.
Update the table
From A to B  From B to A  
B alone  S alone  Downstream (B+S)  Upstream (BS)  
Speed  3  2  3+2=5  32=1 
Time  12t  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 12t, 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 (B_{n})
From A to B  From B to A  Special case: A to B  
B alone  S alone  Downstream (B+S)  Upstream (BS)  Downstream (B_{n}+S)  
Speed  3  2  5  1  (B_{n}+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 “kilometerhour format OR metresecond 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
(B_{n}+2) x 100/60=10
(B_{n}+2) =60×10/100
(B_{n}+2) =6
B_{n}=62
B_{n}=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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