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

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

$\begin{gathered} \mapsto \bf \purple{ \boxed{ \bigstar \bf \: Distance = Speed \times Time }} \\ \end{gathered}</p><p> </p><p>$

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

ACQ

$\begin{gathered} \therefore \tt 8(x - 2) = 7(x + 2) \\ \tt \twoheadrightarrow8x - 16 = 7x + 14 \\ \tt \twoheadrightarrow8x - 7x = 14 + 16 \\ \tt \twoheadrightarrow \: x = 30\end{gathered}$

$\begin{gathered} \therefore \underline{ \green{ \bf \: Speed \: of \: boat \: in \: still \: water = 30 \: kmph }} \\ \end{gathered}$

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

$</p><p>\begin{gathered} \sf \: Distance = 7(x + 2) \: km\\ \dashrightarrow \sf \: 7(30 + 2)\: km\\ \sf \dashrightarrow \: 7 \times 32\: km \\ \dashrightarrow \bf \fcolorbox{purple}{pink}{224 \: km}\end{gathered}$