Question

A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in same time. Find the speed of the still water and speed of the stream

Answer 1

Answer:

speed of boat in still water = 6km/h

Speed of stream = 2km/h

Step-by-step explanation:

Answer 2

Let,

• speed of boat be, x km/hr
• speed of stream be, y km/hr

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Now,

speed of boat upstream = (x - y) km/hr

speed of boat downstream = (x + y) km/hr

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We know that,

speed = Distance/Time

So,

Time = Distance/Speed

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Case 1

When boat goes upstream,

• Distance = 12km
• Speed = (x - y) km/hr

T = 12/(x - y) ........(1)

When boat goes downstream,

• Distance = 40km
• Speed = (x + y) km/hr

T = 40/(x + y) .....(2)

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Total time = 8hrs,

So from (1) and (2),

$\rightarrow \frac{12}{x - y} + \frac{40}{x + y} = 8 \: ......(3)$

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Case 2

When boat goes upstream,

• Distance = 16km
• Speed = (x - y) km/hr

T = 16/(x - y) .........(4)

When boat goes downstream,

• Distance = 32km
• Speed = (x + y) km/hr

T = 32/(x + y) .......(5)

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Total time = 8hrs

So, From (4) and (5),

$\rightarrow \frac{16}{x - y} + \frac{32}{x + y} = 8 \: ......(6)$

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In (3) and (6),

Let,

• 1/(x - y) = u
• 1/(x + y) = v

On substituing these values,

12u + 40v = 8 ......(7)

16u + 32v = 8 ......(8)

divide (7) by 4 and divide (8) by 8,

3u + 10v = 2 ........(9)

2u + 4v = 1 .........(10)

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Solving by Elimination method

=> eq.(9) x 2 and eq.(10) x 3

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6u + 20v = 4

6u + 12v = 3

(-) (-) (-)

--------------------

8v = 1

v = 1/8

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substituing value of v in eq. (10)

2u + 4(1/8) = 1

2u + 2(1/4) = 1

2u + (1/4) = 1

(4u + 1)/2 = 1

4u + 1 = 2

4u = 2 - 1

4u = 1

u = 1/4

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1/(x + y) = v

1/(x + y) = 1/8

x + y = 8 ...............(11)

1/(x - y) = u

1/(x - y) = 1/4

x - y = 4 ...............(12)

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Solving eq. (11) and eq. (12)

x + y = 8

x = 8 - y

substituing x in (12)

8 - y - y = 4

8 - 2y = 4

-2y = 4 - 8

-2y = -4

y = -4/-2

y = 2

And

x = 8 - y

x = 8 - 2

x = 6

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•°• Speed of boat = 6km/hr

Speed of stream = 2km/hr