Question

A steamer goes downstream from one port to another in 6 hours. It covers the same distance in 7 hours. If the speed of the stream be 2 km/hr, find the speed of the steamer in still water.​

Answer 1

Let the Speed of the Steamer in still water be : S kmph

Let the Distance between the two ports be : D km

Given : Speed of the Stream = 2 kmph

★  While moving upstream, As the Stream flows in the direction opposite to the motion of the Steamer. The Stream opposes the motion of the Steamer.

Speed of the Steamer while moving upstream will be :

★  Speed of the Steamer in still water - Speed of the Stream

$:\implies$  Speed of Steamer while moving upstream = (S - 2) kmph

★  While moving downstream, As the Stream flows in the direction of the motion of the Steamer. The Stream supports the motion of the Steamer.

Speed of the Steamer while moving downstream will be :

★  Speed of the Steamer in still water + Speed of the Stream

$:\implies$  Speed of Steamer while moving downstream = (S + 2) kmph

Given : Steamer goes downstream from one port to another in 6 hours

$\bigstar\;\;\textsf{We know that : \boxed{\mathsf{Speed = \dfrac{Distance\;traveled}{Time\;taken}}}}$

$\mathsf{\implies S + 2 = \dfrac{D}{6}}$

$\mathsf{\implies D = 6(S + 2)}$

Given : Steamer covers the same distance upstream while returning in 7 hours (As while going it was downstream, while returning it will be upstream)

$\mathsf{\implies S - 2 = \dfrac{D}{7}}$

$\mathsf{\implies D = 7(S - 2)}$

As, Distance covered during upstream and downstream are Equal :

$:\implies$  6(S + 2) = 7(S - 2)

$:\implies$  6S + 12 = 7S - 14

$:\implies$  7S - 6S = 14 + 12

$:\implies$  S = 26

Answer : Speed of the Steamer in still water = 26 kmph

Answer 2

Step-by-step explanation:

please add brainlist answer

SAMEER RAJ