Question

A motor boat covers a certain distance downstream in a river in 5 hours, It covers the same distance upstream in 6 hours. The speed of water is 2 km/hr. Find the speed of the boat in still water.​

Answer 1

Step-by-step explanation:

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Answer 2

${\pmb{\underline{\sf{ Required \ Solution ... }}}}$

• Time taken to cover Downstream in a river in 5 hours.
• It covers same distance Upstream in 6 hours.
• Speed of water is 2 km/hr

$\\ {\pmb{\underline{\sf{ Assumption ... }}}}$

• Let the Distance be D

• Let the Speed of the Boat in still water be x

$\\ {\pmb{\underline{\sf{ Actual \ Calculation... }}}}$

As We know that: Certain Distance covered in definite Period of Time by Boat.

$\circ \ {\underline{\boxed{\sf\gray{ Time = \dfrac{Distance}{Speed} }}}}$

We have that:

• Speed For Upstream = (x - 2) km/hr
• Speed For Downstream = (x + 2) km/hr

$\colon\implies{\sf{ \dfrac{D}{x-2} = 6 }} \\ \\ \colon\implies{\sf{ D = 6(x-2) }} \\ \\ \colon\implies{\sf{ D = 6x - 12 \ \ \ \ \ \cdots(1) }} \\ \\ \colon\implies{\sf{ \dfrac{D}{x+2} = 5 }} \\ \\ \colon\implies{\sf{ D = 5(x+2) }} \\ \\ \colon\implies{\sf{ D = 5x + 10 \ \ \ \ \ \cdots(2) }}$

We also Know that Distance travelled in both cases is same as Question said above. So, We can compare both Equations to get Actual value of Distance travelled by Boat.

$\colon\implies{\sf{ 5x+ 10 = 6x - 12 }} \\ \\ \colon\implies{\sf{ 10 + 12 = 6x-5x }} \\ \\ \colon\implies{\underline{\underline{\boxed{\sf\pink{ x = 22 \ km/hr }}}}}$

Hence,

${\pmb{\underline{\sf{ The \ Speed \ of \ the \ Boat \ in \ still \ water \ is \ 22 \ km/hr . }}}} \bigstar$