A motor travels 10 mph in still water. The boat takes 4 hours longer to travel 48 miles going upstream than it does to travel 24 miles going downstream. Find the rate of the current.

Answers

Answer 1

Answer:

The rate of the current is 2 mph.

Step-by-step explanation:

When the boat travels upstream we have:

[tex] v_{T_{1}} = v_{b} - v_{c} [/tex]                      

[tex] \frac{x_{1}}{t_{1}} = v_{b} - v_{c} [/tex]    

Where:

[tex] v_{T}[/tex]: is the total speed

[tex]v_{b}[/tex]: is the speed of the boat = 10 mph

[tex]v_{c}[/tex]: is the speed of the current

x: is the distance

t: is the time

And when the boat travel downstream we have:

[tex]v_{T_{2}} = v_{b} + v_{c}[/tex]        

[tex] \frac{x_{2}}{t_{2}} = v_{b} + v_{c} [/tex]                              

Since the boat takes 4 hours longer to travel 48 miles going upstream than it does to travel 24 miles going downstream we have:

[tex] \frac{x_{1}}{t + 4} = v_{b} - v_{c} [/tex]   (1)

[tex] \frac{x_{2}}{t} = v_{b} + v_{c} [/tex]   (2)

By adding equation (1) with (2):

[tex] \frac{x_{1}}{t + 4} + \frac{x_{2}}{t} = 2v_{b} [/tex]

[tex] tx_{1} + (t+4)x_{2} - 2v_{b}t(t+4) = 0 [/tex]

[tex] 48t + 24(t+4) - 2*10t(t+4) = 0 [/tex]

By solving the above equation for t we have:

t = 2 h      

Now, by entering "t" into equation (2) we have:

[tex] \frac{24 miles}{2 h} = 10 mph + v_{c} [/tex]  

[tex] v_{c} = 2 mph [/tex]

               

Therefore, the rate of the current is 2 mph.

I hope it helps you!  


Related Questions

what is : 20.0g of C4H10

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Answer:

20 grams of butane

Step-by-step explanation:

C4H10 is butane

What is the LCM (Least Common Multiple) Of 10, 5, and 6?

Answers

Answer:

30

Step-by-step explanation:

10= 10 20 30

6= 6 12 18 24 30

5= 5 10 15 20 25 30

Which expression shows the result of applying the distributive property to 9(2+5m)?


18 + 45m

2 + 45m

18 + 5m

11 + 14m

Answers

Answer: A: 18 + 45m

Step-by-step explanation:

9(2+5m) = (9 x 2) + (9 x 5m) which gives you: 18 + 45m

Answer:

I think it's 18+45m

Step-by-step explanation:

I just multiplied 9x2 and 9x5.

Graph this inequality:
-15y > 30x - 45

Answers

Answer:

Hope this helped

Twelve decreased by twice a number equals -34 ​

Answers

Answer:

-22

Step-by-step explanation:

-34+12=-22

PLS HELP I WILL GIVE BRAINLIEST

Answers

Answer:

Option 2: y = 6x + -4

Step-by-step explanation:

y = mx + b

y = 6x + -4

Answer:

#2

Step-by-step explanation:

[tex](x^5)(4^3x^7)^0[/tex]

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Answer:

=x⁵

Step-by-step explanation:

that the answer

have a great day

24 is 4 times as great as
Pls help

Answers

Answer:

6=k

Step-by-step explanation:

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Answers

Answer:

B

Step-by-step explanation:

Answer:

48to41, 48:41, 48/41

Step-by-step explanation:

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48to41, 48:41, 41/48

A self-serve frozen yogurt store sells servings up to 12 ounces. It charges $0.50 per ounce for a serving between 0 and 8 ounces, and $4 for any serving greater than 8 ounces and up to 12 ounces.


Build the function that models the relationship between the price p(w) and of the weight w of a serving of yogurt.

Answers

Answer:

p(w) - - - - - - p = 0.5w ; for 0 < w ≤ 8

p(w) - - - - - - p = 4 ; for w < 8 and w ≤ 12

Step-by-step explanation:

Price, p of weight of a toughurt serving :

p(w) - - - - - - p = 0.5w ; for 0 < w ≤ 8

p(w) - - - - - - p = 4 ; for w < 8 and w ≤ 12

The function that models the relationship is:

p(w) = 0.50w  for 0  <  w  ≤ 8

p(w) = 4w   for  8 < w ≤ 12

The self-serve frozen yoghurt store charges:

$0.50 per serving for a serving between 0 and 8 ounces

$4 per serving for any serving greater than 8 ounces and up to 12 ounces.

Let the weight of servings be represented by w

Let the price as a function of the weight be p(w)

For a charge of $0.50 per serving:

p(w)  =  0.50w,  where   0  <  w  ≤ 8

For a charge of $4 per serving:

p(w) = 4w, where 8 < w ≤ 12

Therefore, the function that models the relationship is:

p(w) = 0.50w  for 0  <  w  ≤ 8

p(w) = 4w   for  8 < w ≤ 12

Learn more on functions here: https://brainly.com/question/10439235

PLEASE HELP!!!!!!!!!!!!!!!!​

Answers

Since the angle measures for angle K and angle M are the same, you can set the side lengths equal to each other and solve.

4x+1=3x+17

Subtract 3x from both sides

x+1=17

Subtract 1 from both sides

x=16
The length of side NK is 16

This triangle can only have one altitude.

A.True
B. False
C.It can have four

Help please.

Answers

Answer:

(B) false, because triangle have three altitude.

B. False because I just did this question and I got it right

can someone help me ​

Answers

Answer:

6.6

Step-by-step explanation:

I'm just guessing because it's just adding 1.1 everytime

Kevin has $100 in a savings account that earns 10% annually. The interest is not compounded. How much will he have in 2 years?

Answers

He will have 220 that is how much he will have

If Kelly wakes up after 6:30, then Kelly will be late to
school.
Kelly woke up at 6:45.
A. Kelly will arrive early to school
B. Kelly will be late to school.
C. Kelly will be on time to school.
D. Kelly will catch the bus to school.

Answers

Answer:She’ll be late to school

Step-by-step explanation:

Kelly will be late (B)

a rectangular tree lot must have a perimeter of 100 yards and an area of at least 500 square yards. Describe the possible lengths of the tree lot

Answers

Answer:

36.18 yd and 13.82yd

Step-by-step explanation:

Area of the rectangular tree = Length * Width

A = LW

perimeter of the rectangular tree = 2(L+W)

Given

Area = 500 square yards and

perimeter = 100yards, then;

100 = 2L+2W

50 = L+W .... 1

500= LW ... 2

From 1, W = 50-L

Substitute into 2;

LW =500

L(50-L) = 500

50L-L² = 500

L²-50L + 500 = 0

Factorize

L = 50±√50²-4(500)/2

L = 50±√2500-2000/2

L = 50±√500/2

L = 50±22.36/2

L = 72.36/2 and 27.64/2

L = 36.18 and 13.82

Hence the possible lengths of the tree lot are 36.18 yd and 13.82yd

Write 63/100 as a decimal

Answers

Answer:

it is 0.63

Step-by-step explanation:

plz give me a brainliest plz

For what value of a must LMNO be a parallelogram?​

Answers

Answer:

a = 2.5

Step-by-step explanation:

For LMNO to be a parallelogram then opposite sides are congruent, so

ON = LM , that is

8b - 1 = 4b + 7 ( subtract 4b from both sides )

4b - 1 = 7 ( add 1 to both sides )

4b = 8 ( divide both sides by 4 )

b = 2

Then

MN = 2b + 1 = 2(2) + 1 = 4 + 1 = 5 , so

2a = 5 ( divide both sides by 2 )

a = 2.5

Thus

For LMNO to be a parallelogram , a = 2.5

The value of a that makes LMNO a parallelogram is 5/2.

What is a parallelogram?

A parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

In a parallelogram, the opposite sides are parallel and equal.

This means,

4b + 7 = 8b - 1

7 + 1 = 8b - 4b

8 = 4b

b = 2

Now,

2a = 2b + 1

2a = 2 x 2 + 1

2a = 4 + 1

2a = 5

a = 5/2

Thus,

The value of a is 5/2.

Learn more about parallelograms here:

https://brainly.com/question/1563728

#SPJ5

HELP PLS QUICK


(03.03 LC)
Look at points C and D on the graph:

What is the distance (in units) between points C and D? Round your answer to the
nearest hundredth. (5 points)

Answers

Answer:

[tex]\displaystyle d \approx 7.07[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Reading a Cartesian planeCoordinates (x, y)

Algebra II

Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Step-by-step explanation:

Step 1: Define

Point C (-2, 0)

Point D (3, 5)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Substitute in points [Distance Formula]:                                                       [tex]\displaystyle d = \sqrt{(3+2)^2+(5-0)^2}[/tex][√Radical] (Parenthesis) Add/Subtract:                                                         [tex]\displaystyle d = \sqrt{(5)^2+(5)^2}[/tex][√Radical] Evaluate exponents:                                                                    [tex]\displaystyle d = \sqrt{25+25}[/tex][√Radical] Add:                                                                                               [tex]\displaystyle d = \sqrt{50}[/tex][√Radical] Simplify:                                                                                         [tex]\displaystyle d = 5\sqrt{2}[/tex][√Radical] Evaluate:                                                                                       [tex]\displaystyle d = 7.07107[/tex]Round:                                                                                                             [tex]\displaystyle d \approx 7.07[/tex]


Natilie invested $200 in a savings account that earned 4% simple interest each year. She invested for
two years without adding or taking money from her account.

A. How much INTEREST has she made? (I=PRT or Interest = Principal x Rate x Time

B. How much money does she have in total? Show work for both

Answers

Answer:

16.32 made in interest

216.32 in total

Step-by-step explanation:

Need help again, I hate this lol

Answers

Answer:

4x+64

Step-by-step explanation:

Perimeter is the sum of all sides so you add all of the expressions together. Then combine like terms, x+x+2x, and 14+14+36. Combine them and you get 4x+64.

What is the y-intercept: y + 2 - X= 0

Answers

Try doing (0,-2) for the y intercept

A storekeeper increased the price of snack by 20%. If the price of a snack (after the increase) is 3.25, what is the original price?

Answers

1.50 - 99C I may be wrong but I tried :)

I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS!!!

What is the factored form of each expression?
24. 20x + 35y
F. 4x + 7y, G. 5xy(4 + 7), H. 5(4x + 7y), I. (20 + 35) · (x + y)

25. 24x + 64y
A. 4(6x + 16y), B. 8(3x + 8y), C. 8xy(3 + 8), D. 3x +

Answer them both please! This is due in 2 minutes!!

Answers

Answer:

The answers are H and A, let me know in a comment if you want me to explain it

WILL GIVE BRAINLIEST find area

Answers

Answer:

[tex] 60 \: {cm}^{2} [/tex]

Step-by-step explanation:

[tex]A = \frac{1}{2} (14 + 6) \times 6 \\ \\ = \frac{1}{2} \times 20 \times 6 \\ \\ = \frac{1}{2} \times 120 \\ \\ = 60 \: {cm}^{2} [/tex]

Write an inequality to match this statement: -7 is located to the right of -10. **Hint** You need to use shift and the comma button or the period button to make the greater than or less than sign. *


please tell the answer and explain how to get it

Answers

Answer:

-7 > -10

Step-by-step explanation:

We just have to compare these two numbers. When you're comparing two negative numbers, the smaller number is the bigger one. Ex. -3 is bigger than -6, so we can say that -3 > -6 (-3 is greater than -6). This means that -7 is larger than -10, which allows you to say that -7 > -10.

which of the following equations has a greater rate of change than what is shown in the graph?

A. y = 65x + 100
B. y = 85x
C. y=50x + 150
D. All of the above​

Answers

Answer:

B

Step-by-step explanation:

change of a = 65

b = 85

c = 50

==> (B) is correct one.

yo i’m stuck hahahelp ASAP -4 3/8 - (-1 1/4)

Answers

Answer:

I hope this helps

Step-by-step explanation:

-3 1/8

The correct answer -3 1/8

311,305,299... find the 32nd term

Answers

Answer:

Step-by-step explanation:

It is an arithmetic sequence with common difference = -6

32nd term = 311 - 31(6) = 125

I NEED UR HELP ILL BE BRAINLISTING YALL!

A market stall holder bought a variety of coloured 'hoodies' to sell. Each hoodie costs the stall holder $20 and she intends to sell them to the public at a mark up of 65%

1) calculate the value of the markup on each hoodie.

Answers

Their will be an additional cost of $13 per hoodie.

Answer: $13

Step-by-step explanation:

The markup would be 65% of 20

65% as a decimal is 0.65

0.65*20= 13

The new price would be $33, the markup would be $13

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