Question

A steamer goes downstream from one point to another in 7 hours. It covers the same distance upstream in 8 hours. If the speed of stream be 2 km/h, find the speed of the steamer in still water and the distance between the ports.​

Answer 1

Answer:

Let the distance between the two ports be x km.

Then, speed downstream = x4

And speed upstream = x5

Therefore, Speed of the stream = 12 [speed downstream + Speed upstream]

= 12(x4−x5)

12(5x−4x20)=2

x40=2 = 80 km

Step-by-step explanation:

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Answer 2

Answer:

Speed of boat in still water = 30 kmph

Distance = 224 km

Step-by-step explanation:

Given:-

• A steamer goes downstream from one point to another in 7 hours. It covers the same distance upstream in 8 hours. If the speed of stream be 2 km/h.

To Find:-

• The speed of the steamer in still water and the distance between the ports.

Solution:-

$\bf \: Let$

• The speed of steamer in still water be x km/hr
• Speed in downstream = (x+2) km/hr

As we know that

$\mapsto \bf \purple{ \boxed{ \bigstar \bf \: Distance = Speed \times </strong><strong>Time</strong><strong>}}$

$\sf \clubs \: Distance \: covered \: while \: downstream \\ \red{ : \longmapsto \: \bf 7(x + 2) \: km }\\ \\ \clubs \: \sf Distance \: covered \: while \: upstream \\ \red{ : \longmapsto \bf \: 8(x - 2)}$

ACQ

$\therefore \tt 8(x - 2) = 7(x + 2) \\ \tt \twoheadrightarrow8x - 16 = 7x + 14 \\ \tt \twoheadrightarrow8x - 7x = 14 + 16 \\ \tt \twoheadrightarrow \: x = 30$

$\therefore \underline{ \green{ \bf \: Speed \: of \: boat \: in \: still \: water = 30 \: </strong><strong>kmph</strong><strong>}}$

Now, to find the distance we can put any value of distance given above.

$\sf \: Distance = 7(x + 2) \: km\\ \dashrightarrow \sf \: 7(30 + 2) \: km\\ \sf \dashrightarrow \: 7 \times 32 \: km \\ \dashrightarrow \bf \fcolorbox{purple}{pink}{224 \: km}$