Question

A steamer goes downstream and covers the distance between two ports in 6hours. While it covers the same distance upstream in 8 hours If the speed of stream is 2km/hr find the speed of steamer in still water​

Answer 1

$.$Correct option is 18 km/hr

Let the speed of the steamer in still water be x km/h.

Then, the speed downstream =(x+2) km/h

and the speed upstream =(x−2) km/h

Given, distance covered in 4 hours downstream = distance covered in 5 hours upstream

∴ 4(x+2)=5(x−2)

⇒4x+8=5x−10

⟹4x−5x=−10−8

[Transposing 5x to LHS and 8 to RHS]

⟹−x=−18 (or) x=18km/h

✨❤️ hope helpful ❤️✨

Answer 2

Question:

A steamer goes downstream and covers the distance between two ports in 6hours. While it covers the same distance upstream in 8 hours If the speed of stream is 2km/hr find the speed of steamer in still water

Given:

Distance covered in Downstream= $6hrs$

Distance covered in Upstream =$8hrs.$

To Find:

The speed of steamer in still water

Solution:

Let the speed of streamer in still water be $x km/hr.$

Then,

Speed Upstream= $(x-2)km/hr$

Speed Downstream= $(x+2)km/hr$

We know that,

$\mathsf{Distance=speed×time}$

Also,

$\mathsf{Distance\: covered\: in\: 6hrs.\: downstream=Distance\: covered\: in\: 8hrs.\: upstream}$

$\therefore$ $\mathsf{6(x+2)=8(x-2)}$

ㅤㅤㅤㅤ$:\implies$ $6x+12=8x-16$

ㅤㅤㅤㅤ$:\implies$ $12+16=8x-6x$

ㅤㅤㅤㅤ$:\implies$ $28=2x$

ㅤㅤㅤㅤ$:\implies$ $\large\frac{28}{2}=x$

ㅤㅤㅤㅤ$:\implies$ $\underline\color{red}\boxed{x=14}$

Therefore the speed of steamer in still water is $14km/hr$

Final Answer:

The speed of Streamer in still water is $\mathsf{14km/hr}$

Abbreviation:

$\mathsf{km}$ = Kilometres

$\mathsf{hr/hrs}$ = Hour/hours

More to know:

In solving problems based on time, distance and speed, we use the following formulae:

ㅤㅤㅤ$-$$\mathsf{Distance=Speed×Time}$

ㅤㅤㅤ$-$$\mathsf{Time=\large\frac{Distance}{Speed}}$

ㅤㅤㅤ$-$$\mathsf{Speed=\large\frac{Distance}{Time}}$

Also if,

$\mathsf{Speed\: of\: boat\: in\: still\: water=u\:km/hr.}$

and,

$\mathsf{Speed\: of\: current=v\: km/hr}$

Then,

$\mathsf{Speed\: Upstream=(u-v)km/hr}$

$\mathsf{Speed\: Downstream=(u+v)km/hr.}$