Two tourists went on a hike at dawn. One went from a to b and another one went from b to a. They met at noon but did not stop and continued walking maintaining same speed for the whole trip. One finished his hike at 4pm in B and another one came to A at 9 pm. At what hour was dawn that day?

Answers

Answer 1
Dawn was at 6 am. Variables a = distance from a to passing point b = distance from b to passing point c = speed of hiker 1 d = speed of hiker 2 x = number of hours prior to noon when dawn is The first hiker travels for x hours to cover distance a, and the 2nd hiker then takes 9 hours to cover that same distance. This can be expressed as a = cx = 9d cx = 9d x = 9d/c The second hiker travels for x hours to cover distance b, and the 1st hiker then takes 4 hours to cover than same distance. Expressed as b = dx = 4c dx = 4c x = 4c/d We now have two expressions for x, set them equal to each other. 9d/c = 4c/d Multiply both sides by d 9d^2/c = 4c Divide both sides by c 9d^2/c^2 = 4 Interesting... Both sides are exact squares. Take the square root of both sides 3d/c = 2 d/c = 2/3 We now know the ratio of the speeds of the two hikers. Let's see what X is now. x = 9d/c = 9*2/3 = 18/3 = 6 x = 4c/d = 4*3/2 = 12/2 = 6 Both expressions for x, claim x to be 6 hours. And 6 hours prior to noon is 6am. We don't know the actual speeds of the two hikers, nor how far they actually walked. But we do know their relative speeds. And that's enough to figure out when dawn was.

Related Questions

Sam packed 42kg of rice into one big bag and 6 small ones which are of the same size. the big bag contained 3/7 of the rice. how many kilograms of rice did each small bag contained?

Answers

if the big bag contained 3/7 of the rice, then the smaller bags contained 4/7.
so the smaller bags contained : 4/7(42) = 168/7 = 24 kg.....and their are 6 small bags...so each bag contained : 24/6 = 4 kg per bag <==

A man bought a horse and carriage for $500 paying three times as much for the carriage as for the horse how much did each cost

Answers

Hello! So, in order to solve this question, we should do 500/4. 500/4 = 125. Multiply 125 by 3 and you get 375. The horse costs $125 and the carriage costs $375.
the horse was $125  and carriage  was $375

Solve each data for x: (a) a rectangle has (2x + 1) and (x +2) as length and width. Its area is 77 (b.) a triangle has (2x+2) and (x+3) as base and height. Its area is 35

Answers

area of a rectangle: A= Length*width
(2x+1)(x+2)=77
2x^2+4x+x+2=77
2x^2+5x+2=77
2x^2+5x-75=0
(x-5)(2x+15)=0
x=5 or x=-7.5
Length cannot be negative, so x=5 only
the length is 11, the width is 7
Next, let's look at the triangle.
Area of a triangle: A=1/2 of base*height
(1/2)(2x+2)(x+3)=35
2x^2+8x+6=70
2x^2+8x-64=0
x^2+4x-32=0
(x-4)(x+8)=0
x=4
the base is 10, the height is 7

five cakes cost £4.00 how much do 7 cost

Answers

Greetings!

We can solve this by creating an algebraic equation.
[tex]5/4=7/x[/tex]
Cross Multiply.
[tex]5*x=4*7[/tex]
[tex]5x=28[/tex]
Divide both sides by 5.
[tex](5x)/5=(28)/5[/tex]
The Answer Is:
[tex]x=5.6[/tex]

Seven cakes would cost $5.60.

Hope this helps.
-Benjamin

Footrace takes place among 4 runners, how many ways to finish the race

Answers

4 * 3 *2 *1 = 24 different ways

In an equilateral triangle, what is the relationship between the length of a side and the perimeter?

Answers

1:3
If each side is x, the the perimeter is 3x.  x/3x = 1/3

Answer:

1:3

If each side is x, the the perimeter is 3x.  x/3x = 1/3

Step-by-step explanation:

A tennis supply store pays a wholesaler 90 for a tennis racquet and sells it for 144 what is the markup rate

Answers

uh i dont know if its multiplication or subtraction

Write the equation in slope-intercept form of the line that has a slope of -3 and contains the point (4, -5).

Answers

y-(-5) = -3(x-4)
y+5= -3x +12
y= -3x +7

jill is applying for a car loan. which individual will run her credit report to determine if she's eligible for a car loan?
a. creditor
b. government representative
c. employer
d. landlord

Answers

a creditor will run her report,

 creditor = credit report.

Answer:

a) Creditor

Step-by-step explanation:

a) Right. Creditor

She's applying for a Car loan, the Creditor, i.e. the one who is going to lend her the money to buy a new car. In this case, if Jill is applying to a bank . The creditor will be the Bank she's applying for.

Let's look a the definition of Creditor:

A creditor is a person or company that provides credit to another person or company functions as a creditor.

creditor. (n.d.) Lightbulb Press Dictionary of Financial Terms. (2008). Retrieved September 18, 2019

b) Wrong. There is no direct cause-effect relation since a Government Representative might describe virtually any public civil servant. And also her application has nothing to do with Public Funding.

c) Wrong. Her employer is not the person appointed to determine if she's able to receive the loan. As her boss He/She whether Jill is eligible for a car loan.

d) Wrong. Similarly, her landlord is not the person appointed to determine if she's able to receive the loan.

Find two consecutive positive even integers whose product is 168

Answers

Hello There!

The integers you are looking for are 12 and 14.

Hope This Helps You!
Good Luck :) 

- Hannah ❤

The measures of two complementary angles are in the ratio of 5:7. what is the measure of the smaller angle?

Answers

Final answer:

To find the measure of the smaller angle with a ratio of 5:7 in two complementary angles, set up an equation based on the sum of 90 degrees, leading to a solution where the smaller angle measures 37.5 degrees.

Explanation:

The question asks to find the measure of the smaller angle when two complementary angles have a ratio of 5:7. To solve this problem, we recall that complementary angles sum up to 90 degrees. Since the angles are in a ratio of 5:7, we can denote the measures of the smaller and larger angles as 5x and 7x, respectively.

By combining these ratios, we have 5x + 7x = 90 degrees, which simplifies to 12x = 90 degrees. Solving for x gives us x = 90 / 12 = 7.5. Therefore, the measure of the smaller angle is 5x = 5 × 7.5 = 37.5 degrees.

MATH HELP PLEASE !!!!!!!!!

Answers

3.14 *2r = 157

divide both sides by 3.14

2r = 157/3.14 =50

2r=50

divide both sides by 2

r = 50/2 =25

r = 25

sylvie finds the solution to the system of equations by graphing.

y=2/3x+1 and y=-2/3x-1

which graph shows the solution to sylvie’s system of equations?

a) graph 1
b) graph 2
c) graph 3
d) graph 4

Answers

c) graph 3
Point 3,3 satisfies y=2/3x+1 

Answer:

solution is (-1.5,0)

Graph 3

Step-by-step explanation:

[tex]y=\frac{2}{3}x+1[/tex]and [tex]y=-\frac{2}{3}x-1[/tex]

In the first equation [tex]y=\frac{2}{3}x+1[/tex]

slope = 2/3 and y intercept is 1

Lets start with graphing y intercept +1  

then we slope , move 2 units up and 3 units to the right. stop at (3,3)

Now we graph the second equation

[tex]y=-\frac{2}{3}x-1[/tex]

slope = -2/3 and y intercept is -1

Lets start with graphing y intercept -1  

then we slope , move 2 units down and 3 units to the right. stop at (3,-3)

both graph intersects at a point (-1.5,0)

What is the midpoint m given p(-1, 2) and q(-2, -4)?

Answers

Midpoint = x1+x2/2 , y1+y2,2
= -1 + -2/2 , 2 + (-4)/2 
= -3/2,-1 
= -1.5, -1 

evaluate g(x)=3x+1 over the domain of g, {0,1,2,3}. What is the range of g?

Answers

You can do a table like this:

x        g(x) = 3x + 1

0        3(0) + 1 = 0 + 1 = 1

1        3(1) + 1 = 3 + 1 = 4

2        3(2) + 1 = 6 + 1 = 7

3        3(3) + 1 = 9 + 1 = 10

Then, the range is {1, 4, 7, 10}

Remember, the domain is the set of x values for which the function is defined, and the range is the set of images.

Answer: {1, 4, 7, 10}

The sum of a number and its reciprocal is 13/6. find the number

Answers

suppose the number is x, its reciprocal is 1/x
x+1/x=13/6
(x^2+1)/x=13/6
6(x^2+1)=13x
6x^2-13x+6=0
(3x-2)(2x-3)=0
x=2/3 or x=3/2

A family paid 28,800 as a down payment for a home if this represents 16% of the price of the home find the price of the home

Answers

divide the down payment by the percentage

28,800 / 0.16 = 180,000

 the price of the home is $180,000

To get the price of their home you have to divide the down payment by the percentage to get your answer. 

28,800 ÷ 0.16 = 180,000

 So the price of their home is $180,000.

What is the correct evaluation of 3x2 + 4x - 2y2 + 4y + 5, when x is equal to -1 and y is equal to 5?

Answers

Final answer:

The expression 3x^2 + 4x - 2y^2 + 4y + 5 evaluates to -26 when x = -1 and y = 5.

Explanation:

The evaluation of the expression 3x2 + 4x - 2y2 + 4y + 5 when x is equal to -1 and y is equal to 5 is calculated by substituting these values into the equation.

First, substitute x = -1 into 3x2 + 4x, which gives 3(-1)2 + 4(-1) = 3 * 1 - 4 = 3 - 4 = -1.Next, substitute y = 5 into -2y2 + 4y, which gives -2(5)2 + 4*5 = -2 * 25 + 20 = -50 + 20 = -30.Add up the results from step 1 and step 2, and include the constant 5 from the original expression to find the final result: -1 - 30 + 5 = -26.

Therefore, the correct evaluation of the expression when x = -1 and y = 5 is -26.

To rent a certain meeting room, a college charges a reservation fee of
$
31

and an additional fee of
$
6.60

per hour. The history club wants to spend at most
$
77.20

on renting the meeting room.
What are the possible amounts of time for which they could rent the meeting room?
Use
t

for the number of hours the meeting room is rented, and solve your inequality for
t

.
thank you for your help =)

Answers

31 + 6.60h <=77.20

6.60h <= 46.20

46.20/6.60 = 7

 they can rent up to 7 hours

answer math question, 50 pts for brainliest

Answers

slope = (71.75 - 41)/(7 - 4) = 30.75 /3 = 10.25

answer is B.
the slope is 10.25. This means that Dante earns $10.25 each hour

71.75-41 = 30.75

7-4=3

30.75 / 3 =10.25

 slope is 10.25

 Answer is B

is -22 an irrational number???

Answers

-22 is not an irrational number     





no its a rational number

Sonia has three bracelets. she wears them all at the same time but in a diffrient order each day how many diffrent bracelet combinations dose sonia have to chose from?

Answers

There are 3 bracelets.
The first bracelet can occupy a position in 3 ways.
The second bracelet can occupy the remaining 2 positions in 2 ways.
The third bracelet can occupy the remaining position in 1 way.
The total number combinations is
3*2*1 = 6

Answer: 6

Classify the triangle formed by the given side lengths:
3, 4, 6
a. right triangle
b. acute triangle
c. obtuse triangle
d. not a triangle

Answers

acute because 3+4+6 gives me 13 which is less than 90 so acute would be your answer

What is the shape of a parallel cross section of a sphere?

Answers

The answer is a circle. Hope this helped :)
a sphere is round so when you take a cross section it would be a circle

The leg of a right triangle is 3 units and the hypotenuse is 7 units. What is the length, in units, of the other leg of the triangle?

4
Square root of 40
Square root of 58
10

Answers

7^2 = 3^2 +x^2

49 = 9 +x^2

x^2 = 49-9 =40

x = square root of 40

Answer:

the square root of 40 is the answer your looking for

Step-by-step explanation:

write 25.784 in expanded form

Answers

No expanded form is when all the numbers are broke up
I will be writing the 3 different types of expanded form's

Expanded Notation Form: 

20+5 + 0.7 + 0.08

Expanded Factors Form:
 2 × 10 + 5 × 1 + 7 × 0.1 + 8 × 0.01 + 4 × 0.001

Expanded Exponential Form:

2 × 101 + 5 × 100 + 7 × 10-1 + 8 × 10-2 + 4 × 10-3

Word Form:

twenty-five and seven hundred eighty-four thousandths

What was true about settlement of the louisiana territory?

Answers

The settlers wanted to adopt the same system of slavery in from France. France is one the colonizers who have introduced slavery into their colonies in order to mass produce products like tobacco, wheat and more. France was forced to sell Louisiana on the eve of the revolt of Saint Domingue, one of their colonies in the Caribbean Islands.

Answer:

Settlers in the territory wanted the same approach to slavery as in the states they came from

Step-by-step explanation:

PLEASE HELP!
The prize for winning a contest can be chosen from category A or category B. Prizes from category A have a mean of $1000 and a standard deviation of $50. Prizes from category B have a mean of $1000 and a standard deviation of $300. Describe an advantage of each prize category.

Answers

       x         115
--------- = ------
 216.75   100
216.15*115=249263.25
249263.25/100=249.2625
x= 249.26  B

You eat 3/10 of a pack of hotdogs, your friend eats 1/5 of the pack of hotdogs. what fraction of the hotdogs did you and your friend eat?

Answers

you and your friend ate 1/2 a pack of hotdogs

3/10 + 1/5

(1/5 = 2/10)

3/10+2/10 =5/10 = 1/2

the georges traveled 498.2 miles on 15.8 miles of gas how many miles per gallon did they get to the nearest tenth of a mile?

Answers

31.5 is the gas milage
31.5 
hope this helps!!
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