Question

The speed of a boat in still water is 11 km/hr and the speed of the stream is x km/hr. Find in terms of x, the speed of boat upstream and the speed of boat downstream. If the boat takes 11/4 hours to go 12 km upstream and then return, find the value of x.​

Answer 1

Answer:

x = 5 km / hr.

Hope It helps U Bro

Step-by-step explanation:

Let the speed of the stream be "x km/ hr.n

. Speed of boat in still water = 11 km/ hr.

Therefore, speed of boat upstream = 11 - x

speed of boat downstream = 11 + x

A.T.Q.,12 /11 -x +12/11+x= 2 3/4

⇒12 (1/ 11 -x+1/ 11 +x)= 11 / 4

⇒ 22 / 121 - x2 = 11 / 4*12

⇒ 22/ 121 - x2 = 11 / 48

⇒ 1331 -11 x2 = 1056

⇒ 11 x2 = 275

⇒ x2 = 25

⇒ x = + 5 or - 5

As speed can't be negative, x not equal to -5.

Therefore Speed of stream = x = 5 km / hr.

Answer 2

$\huge\bold\red{Question}$

The speed of a boat in still water is 11 km/hr and the speed of the stream is x km/hr. Find in terms of x, the speed of boat upstream and the speed of boat downstream. If the boat takes 11/4 hours to go 12 km upstream and then return, find the value of x.

$\huge\bold\green{Solution}$

$\sf\color{blue}{Speed\:of\:the\:boat\:upstream =(11−x)\:Km/hr}$

$\sf\color{blue}{Speed \:of \:the \:boat \:downstream =(11+x)\:Km/hr}$

$\sf\color{blue}{Boat\:takes \: \frac{11}{4}\:to\: go \:upstream\: and\: downstream.}$

$\sf\color{blue}{Thus, \: \frac{12}{11 - x} + \frac{12}{11 + x} = \frac{11}{4}}$

$\sf\color{blue}{4(132+12x+132−12x)=11(121− {x}^{2} )}$

$\sf\color{blue}{1056=1331−11x^2}$

$\sf\color{blue}{-11x^2 =-275}$

$\sf\color{blue}{-x^2=-25}$

$\sf\color{blue}{-x=-5}$

$\sf\color{navy}{Speed\: cannot\: be\: negative.}$

$\sf\color{navy}{Thus, Speed\: of\: the\: stream\: is\: 5km/hr}$