Question

can you solve this .....​

Answer 1

Let the Speed of the Stream be : S kmph

Given : Speed of the Boat in still water is 11 kmph

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

Speed of the Boat while moving upstream will be :

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

$:\implies$  Speed of Boat while moving upstream = (11 - S) kmph

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

Speed of the Boat while moving downstream will be :

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

$:\implies$  Speed of Boat while moving downstream = (11 + S) kmph

Given : The Boat travels 12 km upstream

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

$:\implies \mathsf{11 - S = \dfrac{12}{Time\;taken}}$

$:\implies \mathsf{Time\;taken\;to\;travel\;12\;km\;upstream = \bigg(\dfrac{12}{11 - S}\bigg)}$

Given : The Boat returns 12 km downstream

$:\implies \mathsf{11 + S = \dfrac{12}{Time\;taken}}$

$:\implies \mathsf{Time\;taken\;to\;travel\;12\;km\;downstream = \bigg(\dfrac{12}{11 + S}\bigg)}$

Given : Boat takes 2 hours 45 minutes to complete the entire journey (12 km upstream and 12 km downstream to reach it's original point)

It means : Sum of the Time's taken by the boat to travel upstream and downstream to reach it's original point should be equal to 2 hours 45 minutes.

$:\implies \mathsf{\bigg(\dfrac{12}{11 - S}\bigg) + \bigg(\dfrac{12}{11 + S}\bigg) = 2\;hours\;45\;minutes}$

$\bigstar\;\;\mathsf{We\;know\;that : 45\;Minutes\;is\;\bigg(\dfrac{3}{4}\bigg)^{th}\;of\;an\;Hour}$

$:\implies \mathsf{\bigg(\dfrac{12}{11 - S}\bigg) + \bigg(\dfrac{12}{11 + S}\bigg) = \bigg(2 + \dfrac{3}{4}\bigg)}$

$:\implies \mathsf{\bigg(\dfrac{12}{11 - S}\bigg) + \bigg(\dfrac{12}{11 + S}\bigg) = \bigg(\dfrac{11}{4}\bigg)}$

Taking LCM of the fractions of LHS, We get :

$:\implies \mathsf{\bigg(\dfrac{12(11 + S) + 12(11 - S)}{(11 - S)(11 + S)}\bigg) = \dfrac{11}{4}}$

$:\implies \mathsf{12\bigg(\dfrac{11 + S + 11 - S}{11^2 - S^2}\bigg) = \dfrac{11}{4}}$

$:\implies \mathsf{\dfrac{(12 \times22)}{121 - S^2} = \dfrac{11}{4}}$

$:\implies \mathsf{\dfrac{(12 \times2)}{121 - S^2} = \dfrac{1}{4}}$

$:\implies \mathsf{\dfrac{24}{121 - S^2} = \dfrac{1}{4}}$

$:\implies$  121 - S² = (24 × 4)

$:\implies$  S² = 121 - 96

$:\implies$  S² = 25

$:\implies$  S² = (± 5)²

$\mathsf{:\implies S = \sqrt{(\pm\;5)^2}}$

$:\implies$  S = ± 5

$:\implies$  S = 5  (or)  -5

As Speed of the Stream cannot be Negative  $:\implies$  S ≠ -5

$:\implies$  S = 5

Answer : Speed of the Stream = 5 kmph