Question

26. A motor boat whose speed is 15 km /hr is still water goes 30 km downstream and
comes back is a total of 4 hours 30 minutes determine the speed of the stream.
27 Erom the ton a building 16 mhich the anmlar elevation of the ton of hill is 60° and​

Answer 1

Correct Question :

A motor boat whose speed is 15 km/hr is still water goes 30 km downstream and comes back is a total of 4 hours 30 minutes Determine the speed of the stream.

$\rule{100}{2}$

AnswEr :

Let the Speed of Stream be x km/hr and Speed of Boat is given 15 km/hr.

$\bf{ Given}\begin{cases}\sf{Distance = 30 \:km}\\\sf{Downstream = (15 + x) \: km/hr}\\\sf{Upstream = (15 - x) \:km/hr}\end{cases}$

$\rule{200}{1}$

• Let's Head to the Question Now :

$\implies \tt \dfrac{Distance}{Downstream} + \dfrac{Distance}{Upstream} =4hr \:30minutes \\ \\\implies \tt \dfrac{30}{(15 + x)} + \dfrac{30}{(15 - x)} =4\dfrac{1}{2} \\ \\\implies \tt \dfrac{30(15 - x) + 30(15 + x)}{(15)^{2} + {(x)}^{2} } = \dfrac{9}{2} \\ \\\implies \tt \dfrac{450 -\cancel{30x}+ 450 + \cancel{30x}}{225 - {x}^{2}} = \frac{9}{2} \\ \\\implies \tt \dfrac{\cancel{900}}{225 -{x}^{2}} = \dfrac{\cancel9}{2} \\ \\\implies \tt \dfrac{100}{225 -{x}^{2}} = \dfrac{1}{2} \\ \\\implies \tt2 \times 100 = 225 - {x}^{2} \\ \\ \implies \tt200 - 225 = - {x}^{2} \\ \\\implies \tt \cancel- 25 = \cancel- {x}^{2} \\ \\\implies \tt25 = {x}^{2} \\ \\\implies \tt \sqrt{25} = x \\ \\\implies \large \boxed{ \red{\tt x =5 \:km/hr}}$

⠀

∴ Hence, Speed of Stream will be 5 km/hr.

Answer 2

$\huge{\underline{\underline{\mathbb{Answer}}}}$

The speed of stream is 5 km/ hr .

$\huge{\underline{\underline{\mathbb{Solution}}}}$

→Speed of boat in still water = 15 km/hr

→Total time taken ( downstream + upstream) = 4hr30min

$\huge{\underline{\underline{\mathbb{Formulae}}}}$

→ Time = Distance/speed

→ Speed of boat in downstream = ( x+y) where x is still water and y is stream .

→ Speed of boat in upstream = ( x - y ) where x& y are same as above .

Let's assume that the speed of stream is x km/hr

So speed of boat in downstream = ( 15 + x ) km/hr

Speed of boat in upstream =( 15-x ) km/hr

Now we are given with sum total of time taken in covering 30 km distance both in upstream and downstream .

→So time taken during downstream = $\frac{30}{15+x}$

→Time taken while upstream = $\frac{30}{15-x}$

Sum total of time →

$\frac{30}{15 + x} + \frac{30}{15 - x} = 4 + \frac{1}{2}$

→ {30 minutes = 1/2 hr}

$\frac{30(15 - x) + 30(15 + x)}{(15 - x)(15 + x)} = \frac{8 + 1}{2}$

$\frac{450 - 30 + 450 + 30}{225 - {x}^{2} } = \frac{9}{2}$

→ [ (x-y)(X+y) = x² - y² ]

$900 \times 2 = 9(225 - {x}^{2} )$

$9(200) = 9(225 - {x}^{2} )$

$200 = 225 - {x}^{2}$

${x}^{2} = 225 -2 00$

${x}^{2} = 25$

${x}^{2} = {5}^{2}$

$x = 5$

Hence speed of stream ( x km/ hr) = 5 km/ hr