Question

A motor boat whose speed is 180 km/hr. in still water takes one hour more to go 24 km upstream then to return to downstream to same spot, find the speed of stream​

Answer 1

Correct question

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A motor boat whose speed is 18 km/hr. in still water takes one hour more to go 24 km upstream then to return to downstream to same spot, find the speed of stream

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The above correction is made because the given question lead to a weird situation

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A n s w e r

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G i v e n

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• Speed of motor boat in still water is 18 km/hr

• It takes one hour more to go 24 km upstream then to return to downstream to same spot

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F i n d

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• Speed of stream

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S o l u t i o n

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Let the speed of stream be "a"

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$\underline{\bold{\texttt{Speed in upstream :}}}$

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➠ 18 - a

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$\underline{\bold{\texttt{Speed in downstream :}}}$

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➠ 18 + a

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We know that ,

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➠ $\sf T = \dfrac { D } { S }$ ⚊⚊⚊⚊ ⓵

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Where ,

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• T = Time

• D = Distance

• S = Speed

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$\underline{\bold{\texttt{Time taken in Upstream :}}}$

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Let the time taken in upstream be T1

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So ,

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• T = T1

• D = 24

• S = 18 - a

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⟮ Putting the above values in ⓵ ⟯

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➜ $\sf T = \dfrac { D } { S }$

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➜ $\sf T1 = \dfrac { 24 } { 18 - a}$ ⚊⚊⚊⚊ ⓶

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$\underline{\bold{\texttt{Time taken in Downstream :}}}$

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Let the time taken in Downstream be T2

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So ,

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• T = T2

• D = 24

• S = 18 + a

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⟮ Putting the above values in ⓵ ⟯

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➜ $\sf T = \dfrac { D } { S }$

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➜ $\sf T2 = \dfrac { 24 } { 18 + a}$ ⚊⚊⚊⚊ ⓷

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Given that , It takes one hour more to go 24 km upstream then to return to downstream to same spot

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So,

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➜ T1 = T2 + 1

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From ⓶ & ⓷

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➜ $\sf \dfrac { 24 } { 18 - a} = \dfrac { 24 } { 18 + a} + 1$

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➜ $\sf \dfrac { 24 } { 18 - a} = \dfrac { 24 + 18 + a} { 18 + a}$

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➜ $\sf \dfrac { 24 } { 18 - a} = \dfrac { 42 + a} { 18 + a}$

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➜ 24(18 + a) = (18 - a)(42 + a)

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➜ 432 + 24a = 756 + 18a - 42a - a²

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➜ 756 - 24a - a² - 432 - 24a = 0

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➜ -756 + 24a + a² + 432 + 24a = 0

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➜ a² + 48a - 324 = 0

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➜ a² - 6a + 54a - 324 = 0

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➜ a(a - 6) + 54(a - 6) = 0

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➜ (a - 6)(a + 54) = 0

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• a = -54
• a = 6

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As speed can't be negative hence

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➨ a = 6

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∴ The speed of stream is 6 km / hour

Answer 2

Correct question

A motor boat whose speed is 18 km/hr. in still water takes one hour more to go 24 km upstream then to return to downstream to same spot, find the speed of stream

The above correction is made because the given question lead to a weird situation

A n s w e r

G i v e n

Speed of motor boat in still water is 18 km/hr

It takes one hour more to go 24 km upstream then to return to downstream to same spot

F i n d

Speed of stream

S o l u t i o n

Let the speed of stream be "a"

\underline{\bold{\texttt{Speed in upstream :}}}

Speed in upstream :

➠ 18 - a

Speed in downstream :

➠ 18 + a

We know that ,

Where ,

T = Time

D = Distance

S = Speed

Time taken in Upstream :

Let the time taken in upstream be T1

So ,

T = T1

D = 24

S = 18 - a

⟮ Putting the above values

Let the time taken in Downstream

T = T2

D = 24

S = 18 + a

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⟮ Putting the above values in ⓵ ⟯

➜ \sf T2 = \dfrac { 24 } { 18 + a}T2=

18+a

24

⚊⚊⚊⚊ ⓷

Given that , It takes one hour more to go 24 km upstream then to return to downstream to same spot

➜ T1 = T2 + 1

From ⓶ & ⓷

➜ \sf \dfrac { 24 } { 18 - a} = \dfrac { 24 + 18 + a} { 18 + a}

18−a

24 = 18+a

24+18+a

➜ 24(18 + a) = (18 - a)(42 + a)

➜ 432 + 24a = 756 + 18a - 42a - a²

➜ 756 - 24a - a² - 432 - 24a = 0

➜ -756 + 24a + a² + 432 + 24a = 0

➜ a² + 48a - 324 = 0

➜ a² - 6a + 54a - 324 = 0

➜ a(a - 6) + 54(a - 6) = 0

➜ (a - 6)(a + 54) = 0

a = -54

a = 6

As speed can't be negative hence

➨ a = 6

∴ The speed of stream is 6 km / hour