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wlad13 [49]
2 years ago
8

A boat takes 3.6 h to travel downstream from its dock to a fishing hole. If the water were still, it would have taken 4.5 h to m

ake the trip. Let x represent the speed of the boat and let y represent the speed of the water.
(a) Write an expression for the distance traveled in moving water, using 3.6 h for the time. Then write an expression for the distance traveled as if in still water, using 4.5 h for the time.
(b) Set the expressions in Part (a) equal to each other. Then solve the equation for y. Show your work.
(c) What percent of the boat’s speed is the water current?
Mathematics
1 answer:
salantis [7]2 years ago
3 0
Given:

t1 = 3.6 h
t2 = 4.5 h
x = speed of boat
y = speed of water

Required:
a) Expression of distance traveled with moving water with 3.6h
     Expression of distance traveled with moving water with 4.5h
b) Solve for y
c) Percent of boat's speed is the water current

Solution:

Working formula: 
distance = velocity*time

a) For travelling downstream, we get the equation

d = (x +y)*3.6

For travelling upstream, we get the equation

d = (x-y)*4.5

b) Setting the distance as equal for travelling upstream or downstream, we arrive at the equation of

(x+y)*3.6 = (x-y)*4.5
3.6x + 3.6y = 4.5x - 4.5y
8.1y =0.9x
y = x/9

c) percentage = 1/9*100% = 11.1%

<em>ANSWERS: a) d = (x+y)*36; d = (x-y)*4.5
</em>
                     <em>b) y = x/9
</em>                     <em>c) 11.1%</em> 

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9. A ladder of length 23 feet leans against the side of a building. The angle of elevation of the ladder is 76. Find the distanc
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<h3><u>Answer:</u></h3>

  • B) 22.32 feet

\quad\rule{300pt}{1pt}

<h3><u>Solution</u><u>:</u></h3>

we are given that , a ladder is placed against a side of building , which forms a right angled triangle . We wre given one side of a right angled triangle ( hypotenuse ) as 23 feet and the angle of elevation as 76 ° . We can find the Perpendicular distance from the top of the ladder go to the ground by using the trigonometric identity:

\qquad\quad\bull ~{\boxed{\bf{ Sin\theta =\dfrac{Perpendicular}{Hypotenuse}}} }~\bull

Here,

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  • Value of Sin\theta = 0.97
  • Perpendicular = ?

\quad\dashrightarrow\quad \sf { sin\theta =\dfrac{P}{H}}

\quad\dashrightarrow\quad \sf { sin76° =\dfrac{P}{23}}

\quad\dashrightarrow\quad \sf { 0.97=\dfrac{P}{23}}

\quad\dashrightarrow\quad \sf {P = 0.97 \times 23 }

\quad\dashrightarrow\quad \sf { P = 22.32}

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\rule{300pt}{2pt}

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