Boat and Stream Formulas

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.

Example No. 03

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

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Boats and Streams:
Formula:                Boats and Streams Formulas
Solved Examples:  Solved Examples: Set 01
Practice Test:         Practice Test: 01