Question

A steamer goes downstream and covers the distance between two ports in 8 hours while it covers the same distance upstream in 10 hours. If the speed of the stream is 2 km/hr, find the speed of the steamer in still water.

Answer 1

Answer:

Let the speed of the streamer in still water =x km/hr

the speed of the stream is 3 km/hr

Let the distance covered =d km

Speed downstream =x+3 km/hr

Time taken =5 hr

Distance=speed × time

d=5(x+3)

d=5x+15 ............ (1)

Speed upstream =x−3 km/hr

Time taken =7 hr

Distance=speed × time

d=7(x−3)

d=7x−21 ........... (2)

From (1) and (2),

7x−21=5x+15

7x−5x=15+21

2x=36

x=18 km/hr

Step-by-step explanation:

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Answer 2

❖ Given :

• A steamer goes downstream and covers the distance between two ports in 8 hours while it covers the same distance upstream in 10 hours. If the speed of the stream is 2 km/hr.

❖ To Find :

• The speed of the steamer in still water.

❖ Solution :

Let's assume the speed of streamer in still in water be x km/hr

Speed of stream is 2 km/hr.

Therefore,

• Speed downstream = (x + 2) km

• Speed upstream = (x – 2) km

Now, Considering downstream :

$\\ \textsf{The distance covered in 1 hr }= \tt{ (x + 2) \: km} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\\\ \therefore \: \textsf{The distance covered in 8 hrs downstream }= \tt{ 8(x + 2) \: km}$

Similarly, Considering upstream :

$\\ \textsf{The distance covered in 1 hr }= \tt{ (x - 2) \: km} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\\\ \therefore \: \textsf{The distance covered in 10 hrs downstream }= \tt{ 10(x - 2) \: km}$

• Now, Distance covered upstream is same as distance covered downstream .

⠀

$\\ { \purple{ \mathfrak{ \pmb{✰ \: Distance \: \: covered \: \: upstream \: = Distance \: \: covered \: \: downstream \: }}}}$

$\\ \\ \therefore \: \: \: \: \: \tt 10(x - 2) = 8(x + 2)\\ \\ \\ : \implies \tt \: 10x - 20 = 8x + 16 \\ \\ \\ \tt : \implies \: 10x - 8x = 16 + 20 \\ \\ \\ \tt : \implies \: 2x = 36 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt : \implies \: x = \frac{36}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\\ \\ \\ : \implies \:{ \underline{ \boxed{ \mathfrak{ \pmb{ \red{ x = 18}}}}}} \: \: \: \: \pink{\bigstar} \: \: \: \: \: \: \: \: \: \: \: \:$

$\\ \: \: \: { \underline{ \boxed{ \mathfrak{ \pmb { {\therefore{ The \: \: speed \: \: of \: \: water \: \: in \: \: still \: \: water \: \: = \: 18 km/hr .}}}}}}} \: \: \bigstar$