Boats and Streams Important Formulas:-
If ‘x’ is the speed of boat and ‘y’ is the speed of stream,
then
1. Speed in upstream = x
- y
2. Speed in downstream = x + y
3. Speed of boat in still water = 1/2(Speed in upstream + Speed
in downstream)
4. Speed of stream = 1/2(Speed in downstream - Speed in upstream)
5. If the boat goes a certain distance ‘d’ downstream and
returns upstream and total time taken be ‘t’, then, t = {d/(x - y)} + {d/(x + y)}
= (d/upstream)
+ (d/downstream)
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Example No. 01
A boat goes 16 km upstream in 2 hours and downstream in 1 hour. Find how time this boat will take to travel 32 km in all still water?
A. 1.5 hours
B. 2 hours
C. 2 hours 40 minutes
D. 2.5 hours
Answer: Option C
Solution: Speed in upstream = 16/2 kmph = 8 kmph
Speed in downstream = 16 kmph
Speed of boat in still water = 1/2(Speed in upstream + Speed in downstream)
=1/2 (16 + 8) kmph
= 12 kmph
(Or),
x + y = 16/1 =16......... (eq. 1)
x – y = 16/2 = 8........... (eq. 2)
Adding equation (1) and equation (2), we get,
x=12 kmph
Therefore, time taken by the boat to travel 32 km is,
t = 32/12
= 2 hrs 40 min.
Example No. 02
A man goes by motor boat a certain distance upstream at 15 kmph and returns the same downstream at 20 kmph. The total time taken for the journey was 7 hrs. Find how far did he go?
A. 30 km
B. 60 km
C. 90 km
D. 120 km
Answer: Option B
Solution: If the boat goes a certain distance ‘d’ downstream and returns upstream and total time taken be ‘t’, then t = {d/(x - y)} + {d/(x + y)} = = (d/upstream) + (d/downstream)
Therefore, 7 = (d/15) + (d/20)
=> d = 60 km.
A boat moves down the stream at the rate of 1 km in 6 min and up the stream at the rate of 1 km in 10 min. The speed of current is:
A. 2 kmph
B. 2.5 kmph
C. 3 kmph
D. 3.5 kmph
Answer: Option A
Solution:
Speed in downstream = x + y = 1 km / 6 min = 10 kmph............... (eq. 1)
Speed in upstream = x – y = 1 km / 10 min = 6 kmph.................... (eq. 2)
Subtracting equation (2) from equation (1), we get
y= 2 kmph