Question

A steamer goes downstream and covers the distance between two ports and 5 hours while it cover the same distance upstream in 6 hours if the speed of the stream is 2 km per hour find the speed of the stream in still water

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That, Total distance covered is D km, and , speed of steamer in still water is x km/h.

Than,

→ Downstream speed = (x + 2)km/h.

→ Distance = D km.

→ Time = 5 Hours.

→ Distance = Speed * Time.

→ D = 5(x + 2)

→ D = (5x + 10) -------------- Eqn.(1)

Now,

→ Upstream speed = (x - 2)km/h.

→ Distance = D km.

→ Time = 6 Hours.

→ Distance = Speed * Time.

→ D = 6(x - 2)

→ D = (6x - 12) -------------- Eqn.(2)

Comparing Both Eqn. Now, we get,

→ (5x + 10) = (6x - 12)

→ 6x - 5x = 10 + 12

→ x = 22km/h. (Ans.)

Hence, speed of steamer in still water is 22 km/h.

Answer 2

${ \bold{ \huge{ \underline{ \pink{ Question:-}}}}}$

▪ A steamer goes downstream and covers the distance between two ports in 5 hours while it cover the same distance upstream in 6 hours. Find the speed of the stream in still water.

${ \huge{ \bold{ \underline{ \pink{Answer-}}}}}$

▪ Let the total distance covered be ' d ' km and the speed of steamer in still water be ' s ' km/hr ..

${ \bold{ \underline{ \blue{Given-}}}}$

${ \bold{ \bigstar{ \: \: \: for \: downstream}}}$

time taken to cover the distance d km = 5 hour

speed = ( S + 2 ) km/ hr

${ \bold{ \blue{distance = speed \times time}}}$

${ \bold{d = (s + 2) \: km {hr}^{ - 1} \times 5 \: hr}}$

${ \bold{ \implies{d = 5(s + 2)}}}$
_____________________


${ \bold{ \bigstar{ \: \: \: for \: upstream}}}$

time taken to cover the distance d km = 6 hour

speed = ( S - 2) km/ hr

${ \bold{ \blue{distance = speed \times time}}}$

${ \bold{d = (s - 2) \: km {hr}^{ - 1} \times 6 \: hr}}$

${ \bold{ \implies{d = 6(s - 2)}}}$

since,

the distance covers is same for both downstream and upstream....

therefore,

${ \bold{ \pink{d = 5(s+ 2) = 6(s - 2)}}}$

${ \bold{ \implies{5s + 10 = 6s - 12}}}$

${ \bold{ \implies{6s - 5s \: = 10 + 12}}}$

${ \boxed{ \bold{ \implies{ \red{s = 22 \: km {hr}^{ - 1} }}}}}$

hence,

the speed of the stream in still water = 22 km/hr