A motorboat is capable of traveling at a speed of 14 miles per hour in still water. On a particular day, it took 15 minutes longer to travel a distance of 12 miles
upstream than it took to travel the same distance downstream. What was the rate of current in the stream on that day?

Answers

Answer 1

By solving a system of equations we will find that the rate of current in the stream is S = 2 mi/h.

When the motorboat travels downstream, the total velocity will be the velocity of the motorboat in still water plus the velocity of the stream, while if the motorboat travels upstream, we have the velocity of the stream subtracted.

So upstream the speed is:

(14 mi/h - S)

Downstream the speed is:

(14 mi/h + S)

Where S is the rate of current in the stream.

We know that downstream it takes 15 minutes more to travel 12 miles, then we can write the system of equations:

(14 mi/h + S)*T = 12 mi

(14 mi/h - S)*(T - 15 min) = 12 mi

To solve this, we need to isolate one of the variables in one of the equations, I will isolate T in the first one:

T = (12 mi)/(14 mi/h + S)

Replacing that in the other equation we will get:

(14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi

Now we can solve this for S. Now we can multiply both sides by (14 mi/h + S).

(14 mi/h - S)*12 mi  - (14 mi/h + S)*(14 mi/h - S)*(- 15 min) = 12 mi*(14 mi/h + S)

Also notice that the speeds are in hours, so we can rewrite:

- 15 min = -0.25 h

(14 mi/h - S)*12 mi  - (14 mi/h + S)*(14 mi/h - S)*(- 0.25 h) = 12 mi*(14 mi/h + S)

168 mi^2/h - 12mi*S  + 49mi^2/h + 0.25h*S^2 = 168mi^2/h + 12mi*S

- 12mi*S  + 49mi^2/h - 0.25h*S^2 = 12mi*S

-24mi*S -  0.25h*S^2  + 49mi^2/h = 0

This is a quadratic equation, the solutions are:

[tex]S = \frac{24mi \pm \sqrt{(-24mi)^2 - 4*(49mi^2/h)*(-0.25h)} }{2*-0.25h} \\\\S = \frac{24mi \pm 25 mi }{-0.5h}[/tex]

We only take the positive solution, so we get:

S = (24 mi - 25 mi)/(-0.5 mi) = 2 mi/h

The rate of current in the stream is 2 mi/h.

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Related Questions

help me does anyone know the answer to this? what is 4y+13=?

Answers

Answer:

I think Colorfulmusic is correct

Step-by-step explanation:

3.25  I'm pretty sure

Chris drives to a nearby city that is 30 miles away. The average miles per gallon for his car is 20. Gas prices are currently $3.49 per gallon. How much will he spend on gas to drive to the city

Answers

Answer:

5.235 (Simplifies as $5.24)

Step-by-step explanation:

1 gal = 20 miles

1.5 gal = 30 miles

1 gal = $3.49

1.5 gal = $5.235

Pls help I’ll brainlest ASAP


Make this sentence better the building is old and ugly

Answers

Answer:

the building is aged and unique.

PLEASE HELP BRAINLEST TO WINNER!!!!!!!
The coordinates of a point on a coordinate grid are (−1, 5). The point is reflected across the x-axis to obtain a new point. The coordinates of the reflected point are

(1, −5)
(−1, 5)
(1, 5)
(−1, −5)

Answers

(-1, -5)

x-axis is to flip the y - coordinates

y-axis is to flip the x - coordinates

At a local corner store, the cost of a bag of chips at the corner store is $1.30, and the
cost of a banana is $1.40. What would it cost to get 4 bags of chips and 5 bananas?
What would it cost to get a bags of chips and y bananas?
Total cost, 4 bags of chips and 5 bananas:
Total cost, x bags of chips and y bananas:
Submit Answer
attempt 2 out of a problem 1 out of maxi

Answers

Answer:

1- 12.20$

2- 1.30$ + 1.40y$

3- 1.3x + 1.4y

Step-by-step explanation:

input unknown values using x and y

–4x – 5 + 2x = –11
i need help solving for x in this equation

Answers

Answer:

x is 3

Step-by-step explanation:

-2x is -6

2x is 6

x is 3

Answer:

X=3

Step-by-step explanation:

-4(3)=-12

-12-5=-17

2(3)=6

-17+6=-11

Y = ___x + ____

Find the equation of the line.

Answers

Answer: Y=(0,-2)+4G ……

Domain:
Range:
HELP I BEG

Answers

Well if the cubic unit is one, then we can assume that the domain is -1<0

B. Hanapin ang sagot (quotient) gamit ang paghahati-hati. (1 puntos bawat bilang = 5 puntos) 26.4)448 27.800 + 10 = 1 28. 3)663 = 29.56 + 8 = 30. 120 + 6 =​

Answers

answer :

120 + 6 = 126

explanation:

sa calculator lang yan haha jk

pero yan talaga ang sagot promise hindi ako ng bo-bola haha stay safe and stay positive na lang huwag lang sa c o vi d

what is 4% of 32? is it a percent, base, or amount

Answers

Answer:

1.28 - amount

Step-by-step explanation:

You would multiply 32 times 0.04 and get 1.28 which I assume would be an amount.

The amount of 4% of 32 is 1.28.

We have to determine what is 4% of 32.

What is the percentage?

This free percentage calculator computes a number of values involving percentages, including the percentage difference between two given values.

Suppose it is an x percent.

Therefore x multiply 32 times 0.04 and get 1.28 an amount.

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PLEASE HELP ME
It snowed 2/3 of a foot in January and 1/2 of a foot in February. How much more did it snow in January than in February?

Answers

Answer:

Step-by-step explanation:

2/3 - 1/2 ?=?

4/6 - 3/6 = 1/6 ft more

Need help with this assignments

Answers

Given values:-

P= 0.97

V= 2.85

R= 0.082

T= 295

n= ?

we have given formula,

PV=n RT

so,

n = PV/RT

[tex]n = \frac{0.97 \times 2.85}{0.082 \times 295} \\ = \frac{2.7645}{24.19} \\ = 0.1142 \\ = 0.11[/tex]

0.11 is your answer.

What is his error? Try to describe the picture. (Pls help I need 4 pages due tomorrow)

Answers

Answer:

Ben's error is that he thought both pizzas were the same size, well what was left and in the beginning.

Step-by-step explanation:

Even if both 1/4 is left, that doesn't mean you started with the same amount.  Also, both 1/4 pieces are different shapes and sizes, making him wrong.

Hope this helped!! :)

Find the value of X that makes lines L and M parallel.

Answers

Answer:

x = 11

Step-by-step explanation:

    If the lines were parallel, then the transversal would make 2x + 1 and 23° alternate interior angles. Alternate interior angles equal one another, so set up the following equation.

[tex]2x+1=23~(Given)\\\\2x+1-1=23-1~(Subract~1~on~both~sides)\\\\2x=22~(Simplify)\\\\\frac{2x}{2}=\frac{22}{2}~(Divide~2~on~both~sides)\\\\x=11~(Simplify)[/tex]

lol mine looks different

EASY POINTS


f(t)=−3t+4f, left parenthesis, t, right parenthesis, equals, minus, 3, t, plus, 4
f
(
f(f, left parenthesis

)
=
19
)=19right parenthesis, equals, 19

Answers

f() = -5 when f(t) = -3t + 4 is equal to 19. The value of t is -5

The given function is f(t) = -3t + 4. To find the value of f() when it is equal to 19, we substitute 19 in place of f() in the equation.

f() = -3() + 4

Since the value of f() is not provided, we can solve for it by setting the equation equal to 19:

-3() + 4 = 19

To solve for f(), we isolate the variable on one side of the equation. First, we subtract 4 from both sides:

-3() = 19 - 4

-3() = 15

Then, we divide both sides of the equation by -3 to solve for :

/ -3 = 15 / -3

= -5

It's important to note that the notation f() represents the value of the function at a specific point, usually denoted by a specific value in the parentheses. In this case, we were given f() = 19, and our task was to find the corresponding value of . By solving the equation, we determined that = -5 in this scenario.

Therefore, f() = -5 when f(t) = -3t + 4 is equal to 19.

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100 points. Math Question

Answers

The answer is -2. Hope this helps

Answer:

The answer is 2.

Step-by-step explanation:


How much would $100 invested at 6% interest compounded monthly be
worth after 20 years? Round your answer to the nearest cent.

Answers

Answer:

331.02

Step-by-step explanation:

Donny jumped from a rock into a lake. The rock is 35 feet above water. He dove 15 feet below the surface of the water. His brother says he traveled 20 feet in all. Donny says he traveled 50 feet in all. Who correct?

Answers

Donny is correct. To solve this problem all you need to do is add 35 to 15 equation below ⬇️

A rectangular garden is 16 feet wide. Its length is 8 feet more than twice the width. What is the area of the garden?

Answers

Answer:

640 ft²

Step-by-step explanation:

Hi there!

We're given:

Width = 16

Length = 2 x Width + 8

Solve for the length:

l = 2(16)+8

l=32+8

l=40

Therefore, the length of the garden is 40 ft.

To find the area, multiply the length and width:

A = lw

A = (16)(40)

A = 640 ft²

I hope this helps!

solve for x y=c(x+b)

Answers

Step-by-step explanation: To solve for x in this literal equation, I would first distribute the C through the parentheses to get y = cx + cb.

Now subtract cb from both sides to get y - cb = cx.

Finally, divide both sides by c to get y - cb / c = x.

Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 8 people took the trip. She was able to purchase coach tickets for ​$160 and first class tickets for ​$950. She used her total budget for airfare for the​ trip, which was ​$3650. How many first class tickets did she​ buy? How many coach tickets did she​ buy?

Answers

Answer:

Money for coach tickets is $1280 and money for first class is $7600

Step-by-step explanation:

8 x 160 = 1280

8x 950 = 7600

SOmeone help me i'm stuck on thia question

Answers

Answer:

17

Step-by-step explanation:

A triangle has an angle that measures 55°. The other two angles are in a ratio of 11:14. What are the measures of those two angles?

Answers

9514 1404 393

Answer:

  55° : 70°

Step-by-step explanation:

The sum of the two other angles is ...

  180° -55° = 125°

The sum of the ratio units is 11+14 = 25. Each ratio unit stands for 125°/25 = 5°. Then the other two angles are ...

  11×5° = 55°

  14×5° = 70°

Answer:

55° and 70°

Step-by-step explanation:

A triangle has an angle that measures 55°. The other two angles are in a ratio of 11:14. What are the measures of those two angles?

the sum of the internal angles of a triangle is 180 °, we take 55 ° of the known angle and we have the sum of the other two, 125 °, the ratio is 11:14, one is 11 units and one is 14 units, we add them and we divide 125 ° by (11 + 14) = 25 and we have a unit, 125: 25 = 5. now we multiply the unit first by 11 and then by 14 and find the measure of the angles.

11 * 5 = 55°

14 * 5 = 70°

--------------------

check

55 + 55 + 70 = 180°

the sum of the interior angles of a triangle is 180,

so

the answer is good

A car drove 55 miles per hour for 8.2 hours and 75 miles per hour for 3.6 hours. How far did the car drive?

Answers

Answer:

Step-by-step explanation:

So at 38mph you are roughly traveling .6333 miles a minute. So 13 miles would take you roughly 8.2 minutes. How does one figure out this?

We know that there are 60minutes in an hour. We know you’re driving 38miles per hour. Dividing 38 by 60 gives you the miles per minute. Multiple that by how many miles you’re driving to get an estimate of the minutes it takes to drive those miles.

Please help please please help me please help please please

Answers

Answer:

y - 6 = -3 ( x - 7)

Step-by-step explanation:

Use one of the points.

m is the slope

☆Answer : (X1, Y1) = (7, 6) (X2, Y2) = (11, -6)m = -3

Y - Y1 = m(X - X1)

y - 6 = -3(x - 7)

y - 6 = -3x + 21

y - 6 + 3x - 21 = 0

y - 27 + 3x = 0

3x + y - 27 = 0

What is the surface area of the rectangular prism below?

Answers

Answer:

8*8 *2=64

8*19 *2=304

8*19*2=304

672units is your answer

The surface area of the rectangular prism below is 736 square units

Surface area of rectangular prism

The formula for calculating the surface area of the rectangular prism is expressed as:

A = 2(lw + wh + lh)

Given the following parameters

l = 8

w = 19

h = 8

Substitute

SA = 2(8(19) + 8(19) + 8(8))

SA = 2(152 + 152 +64)

SA = 2(304+ 64)

SA = 2(368)

SA = 736 square units

Hence the surface area of the rectangular prism below is 736 square units

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On average, Laylah drinks 1/2 of a 6-ounce glass of water in 2/3 hour. What is 1/2 of 6?

Answers

Answer:3

Step-by-step explanation:

1/2 of 6 is 3 because (6x1)/2=6/2 which equals 3

A child is chosen at random from the group.
a)
What is the probability that the chosen child is a girl?
Give your answer as a fraction.
b)
What is the probability that the chosen child is a left-handed girl?
Give your answer as a fraction.

Answers

Answer:

A. 2/5

B. 1/10

Step-by-step explanation:

First off we need to calculate the probability that the chosen child is a girl So to calculate this probability, we have to know the num. of girls which is seen in the table. There are a total of 8 girls.

Therefore the probability of a girl being chosen is equivalent to the number of girls/exact number of children = 8/20 = 2/5 simplified.

Now to find the probability that the chosen girl is left-handed.

The amount of left-handed girls there is only 2. therefore the probability of selecting a left-handed girl will be 2/20 = 1/10 simplified.

This year, there were 25% fewer sunny days than last year.
The number of sunny days this year is blank% of the number of sunny days last year.

Answers

Please write the full question, you wrote half of the question. If you could write the full one, I could probably be able to answer it

Which of the following statements are true? Select all that apply.

Answers

explain better please?? Thanks

Answer:

They have 2 left one OR 2 right ones are true

Step-by-step explanation:

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