Mathematics Middle School

April can run at a rate that is 2 miles per hour faster then Donna's rate. one day, april gave donna a 25 minute head start on a run. if April passes Donna five miles from the starting point, how fast is each Runner running?

Answers

Answer 1

Let us say that:

s = speed of Donna

s + 2 = speed of April

Then we are also given that:

t + (25/60) = time of Donna

t = time of April

The distance taken by the two should be equal. We know that distance is the product of speed and time, so:

s * (t + 25/60) = (s + 2) t

We also know that:

(s + 2) * t = 5

s = 5/t – 2

So that:

(5/t – 2) * (t + 25/60) = 5

5 + 125/60t – 2t – 50/60 = 5

25/12t – 2t – 5/6 = 0

Multiply everything by t:

- 2t^2 – 5/6 t + 25/12 = 0

t^2 + 5/12 t = 25/24

Completing the square:

(t + 5/24)^2 = 25/24 + (5/24)^2

t + 5/24 = ± 1.04

t = -1.25 h, 0.83 h

Since time cannot be negative, therefore t = 0.83 h

So,

(s + 2) * t = 5

s + 2 = 5/0.83 = 6 miles per hour

s = 4 miles per hour

Answers:

speed of Donna = 4 miles / hr

speed of April = 6 miles / hr

Related Questions

Find the value of x for which l is parallel to m. The diagram is not to scale.

a. 31

b. 62

c. 93

d. 149

Answers

Answer:

The answer would be A because x is the exact same length as the other side which is 31

Step-by-step explanation:

you are choosing between two health clubs. club a offers membership for a fee of $19 plus a monthly fee of $21. club b offers membership for a fee of $13 plus a monthly fee of $22. after how many months will the total cost of each health club be the same? what will be the total cost for each club?

Answers

the price will be the same after 6 months and the total price will be $145.

what is the GCF of 20,36 and 72

Answers

The greatest common factor is four.

The GCF of 20, 36, and 72 would be 4 since 4 can go into 20, 36, and 72 through multiplication and division such as 4 x 5 = 20, 4 x 9 = 36, and 4 x 18 = 72.

Halle is hiking down into a canyon. She descends 3,000 ft in 1 3/4 hours. To the nearest foot, what number shows her descent per hour?

Answers

What we are asked to find out is speed per hour. To find speed, divide distance by time. Distance is 3000 ft and time is 1 3/4 hr. To make calculations easier, let us convert time into minutes. 1 hour is 60 minutes and 3/4 hour is 45 minutes. So total minutes is 105. Now let us divide 3000 by 105. We get 28.57 ft per minute. Now multiply this number by 60 to convert speed per minute into speed per hour. 28.57 * 60 = 1714 ft in 1 hour.

In the table, the parts of strawberry concentrate and the parts of water to prepare a strawberry drink are given. There is a proportional relationship between these two quantities. Find the value of x.

Answers

I think 12. Lol I might be wrong maybe 9 can you list your answers choices?

Answer:

Step-by-step explanation:

its 12 D

the answer to the question

Answers

8*2=16+1=17 over 2
2*4=8+3=11 over 4
17/2 times 11/4=34/4 times 11/4=374/4

A gas station charges $2.20 for each gallon of gasoline how we paid $12.10 for gasoline how many gallons of gasoline did harry bye

Answers

He bought 5 and a half (5.5) gallons.

He bought 5.5 gallons of gas. Plz mark brainliest

Someone please help. I'll mark you as brainliest :)

Answers

Scientific notation are super long numbers that are shortened by a decimal and an exponent. In my opinion, it's much more fun to write zeroes over and over, but nobody cares about my opinion, haha.
So how to make a number a scientific notation:
Step one: Identify the number. (ex. 0.000025)
Step two: Get rid of the zeroes for a second. We will get to that later. (25)
Step three: Put a decimal point between the two numbers. If there are three or more, but the decimal point before the last left number. (2.5)
Step four: Break! (math is boring at times)
Step five: Put the decimal into the scientific notation format. A scientific notation format is _._*10^_. The blanks represent the places that the numbers should go into. The power can be negative or positive, more on that later. For this equation, we will put the decimal before the times 10. (2.5*10^_)
Step six: Now we have to determine the value of the power. That is very easy. First, let’s go back to the decimal. 0.000025. Since we put the after decimal point between 2 and 5, We will count to the other initial decimal point. For this one, there are 5 decimal points. So that means the value of the power is 5. If the original number was positive, you would put the decimal point into the large number, count the number of well….numbers there are between the decimal point and the last number.
Step seven: Set it up! (2.5*10^5)Done!!!
For number two, 2x10^-4(sand)/1x10^-5(cell) = 2x10^1. SO this means the answer is 20 times.

12+4n>44 or 10-12n>-38

Answers

-12 from both sides and -10 from both sides
4n>32 or -22n>-38
divide 4 from both sides and divide -22 from both sides
n>8 or n>1.72...

What is 0.46 repeating as a fraction

Answers

Umm, assuming in this case it would be 0.4646464646464646...

Then you would just assign it a variable in the beginning:

x = 0.46464646...

Then multiply it by 100, to get:

100x = 46.46464646464646...

Now you just want to subtract x from 100x, or

46.464646464646464646... - 0.46464646464646...

Which would result in 99x = 46.

Now just divide 99 from both sides to get:

x = 46/99

So it would be 46/99.

I think.

A(n)___
is a letter used as a placeholder for an unknown value.

Answers

variable
variables are any letters you use, such as in 3x, x is your variable. It holds an unknown value

The answer is a variable! An example of a variable is:
5x +5 =35
X= 6

How can I show my work for 257x66

Answers

Write it as long multiplication with the greater number on top
257
•66
___
Blank

Here is the work shown, sorry if u can't read it I have light hand writing

Ken and Hamid run around a track. It takes Ken 80 seconds to complete a lap. It takes Hamid 60 seconds to complete a lap. Ken and Hamid start running at the same time from the start line. How many laps will they each have run when they next meet on the start line?

Answers

The correct answer is:

Ken will have run 3 laps and Hamid will have run 4.

Explanation:

To find this, we first find the number of seconds that will have passed when they meet again. We use the LCM, or least common multiple, for this. First we find the prime factorization of each number:

80 = 10(8)

10 = 5(2)

8 = 2(4)

4 = 2(2)

80 = 2(2)(2)(5)(2)

60 = 10(6)

10 = 5(2)

6 = 2(3)

60 = 2(2)(3)(5)

For the LCM, we multiply the common factors by the uncommon. Between the two numbers, the common factors are 2, 2 and 5. This makes the uncommon 2, 2, and 3, and makes our LCM

2(2)(5)(2)(2)(3) = 240

This means every 240 seconds they will both be at the start line.

Since Ken completes a lap in 80 seconds, he completes 240/80 = 3 laps in 240 seconds.

Since Hamid completes a lap in 60 seconds, he completes 240/60 = 4 laps in 240 seconds.

Ken will have run [tex]3[/tex] laps and Hamid will have run [tex]4[/tex] laps when they next meet on the start line.

Take LCM of [tex]80,60 =240\\[/tex]

After every [tex]240[/tex] seconds they will both be at the start line.

So in [tex]240[/tex] seconds Ken covered

[tex]\dfrac{240}{80}=3laps\\[/tex]

So in [tex]240[/tex] seconds Hamid covered

[tex]\dfrac{240}{60}=4laps\\[/tex]

Ken will have run [tex]3[/tex] laps and Hamid will have run [tex]4[/tex] Laps.

Learn more about Speed ,time and distance here:

https://brainly.com/question/23774048

Allison has 3 containers with 25 crayons in each.She also has 4 boxes of markers with 12 markers in each box.She gives 10 crayons to a friend. How many crayons and markers does Allison hace now?

Answers

she should have 113 total

25 x 3 is 75, so next, we subtract 10 leaving her with 65 crayons. 12 x 4 is 48, so she has 48 markers. The answer is 65 crayons and 48 markers.

The radius of a DR.PEPPER can is 3 cm and the height is 12 cm. What is the distance from the center of the bottom of the can to the edge of the top of the can?

Answers

Isn't it just 12 cm? Wait no I think it's 11.62

Jeff is baking a cake. The recipe says that he has to mix 32 grams of vanilla powder to the flour. Jeff knows that 1 cup of that particular vanilla powder has a mass of 128 grams. He added two over three of a cup of vanilla powder to the flour. Should Jeff add more vanilla powder to make the exact recipe, or did he go over and by what amount?

Answers

Jeff has added 53.33 grams more vanilla powder than the recipe.

The recipe calls for 32 grams of vanilla powder, and we need to compare this to the amount Jeff used.

Jeff added two-thirds of a cup of vanilla powder to the flour. Since 1 cup of vanilla powder is 128 grams, two-thirds of that amount can be calculated as follows:

(2/3) × 128 grams = 85.33 grams (rounded to two decimal places).

Comparing this to the requested 32 grams, Jeff has added more than the recipe asks for:

85.33 grams - 32 grams = 53.33 grams.

how to solve the equation 9v = 8 + v

Answers

Here are some things you should know when solving algebraic equations.

If you add an expression to both sides of an equation, the resulting equation will have the same solution set as the original equation. In other words, they will be equivalent. This is true for all operations. As long both sides are treated the same, the equation will stay balanced.

You will also need to know how to combine like terms. But what are like terms to begin with? Like terms are defined as two terms having the same variable(s) (or lack thereof) and are raised to the same power. In mathematics, something raised to the first power stays the same. So, 5x and 10x are like terms because they both have the same variable and are raised to the first power. You don’t see the exponents because it doesn’t change the value of the terms.

To combine like terms, simplify add the coefficients and keep the common variable(s) and exponent.

The distributive property is another important rule you will need to understand.

The distributive property is used mostly for simplifying parentheses in expressions/equations.

For example, how would you get rid of the parentheses here?

6(x + 1)

If there wasn’t an unknown in between the parentheses, you could just add then multiply. That is what the distributive property solves. The distributive property states that a(b + c) = ab + ac

So, now we can simplify our expression.

6(x + 1) = 6x + 6

Now let's solve your equation.

9v = 8 + v
8v = 8 <-- Subtract v from each side
v = 1 <-- Divide both sides by 8

So, v is equal to 1.

What’s the smallest value of .50, .00567, .055, and .05

Answers

.00567 Because it’s first digit is in the thousandths place while the others are in the tenths and hundredths.

Sally had 2/9 of a cup of pudding as a snack after school and she had 1/4 of a cup of pudding as dessert after dinner. Sally estimated that that she had about of a cup of pudding today. Is Sally's estimate reasonable?
A.
Yes, because and .
B.
No, because .
C.
Yes, because he added the numerators.
D.
No, because and .

Answers

Sally had about a half cup of pudding. If you make both numbers have the same denominator, you would get 8/36 and 9/36. Add them together, and you get 17/36, which is almost half.

The expression 625(1−x) gives the discounted price of a television, where x is the percent of the discount written in decimal form. What does the 625 represent in the expression?
the original price of the television
the percent of the original price being paid the discounted price of
the television
the percent of discount

Answers

the original price of the television

took the test: Original price of the television

Solve -2.5n + 8.7 > 5.45.

A. n < 1.3
B. n > 1.3
C. n < -5.66
D. n > -5.66

Answers

A. n<1.3

-2.5n+8.7>5.45
subtract 8.7 from both sides
-2.5n>-3.25
divide -2.5 from both sides
(since you divided by a negative you flip the sign!!)
n<1.3

If a revolving restaurant can rotate 270° in 45 minutes, how long does it take for the restaurant to make a complete revolution?

Answers

the answer is one hour. 360-270=90 90 is a fourth of 360. 45 minutes is 3/4 of an hour so yeah

270/360 = 0.75 = 3/4 of a complete revolution

45 minutes = 3/4 of an hour

so it is doing 1/4 of a revolution every 1/4 hour

so it would take 1 hour to do a complete revolution

I need -35+345 and I need to show work

Answers

-35 + 345

345 - 35 =

345
- 35
-----
310

hope this helps

In the expression 5^2, the 2 represents the

Answers

Exponent: amount of times a number is being multiplied

Hope this helps!

In the expression 5^2, the two represents the exponent and the 5 is the base. The exponent shows how many times you have to multiply the base. So 5^2 is equal to 5*5 which equals 25. Hope this helps! =)

Two forms to write the number 304,001

Answers

304001 (number form)

300000 + 4000 + 1 (expanded form)

three hundred four thousand and one (word form)

hope this helps

Find each amount

1/4 of 12 bottles of water =___bottles

2/3 of 24 bananas = ____ bananas

3/5 of $40 restaurant bill = $ ___

5/6 of 18 pencils = ___ pencils

Answers

3 bottles of water 16 bananas $24 and 15 pencils

How do you find the area of a triangle

Answers

1/2(bh)
1/2 times the base times the height

Use the formula:

[tex] \frac{b\: \times \:h}{2} [/tex]

B refers to the base and H refers to the height of the triangle.

As such, multiply both the base and height of the triangle and divide the answer by 2, to find the area of the triangle.

87,628 divided by 931

Answers

Your Answer Is...

94 R 114.

Glad I Could Help, And Good Luck!

My Brainly Name: AnonymousGiantsFan

94.12 unless you need more numbers

A magazine photographed is 24 cm long and 16 write each ratio

Answers

Since the length is 24 and the width is 16, we have the length to width ratio equal to 24/16. Since 8 goes into 24 3 times and into 16 2 times, we have 3/2. For width to length, we have 16/24=2/3 using the same reasoning as last time (except the numerator and denominator are flipped)

Final answer:

The requested ratios of the width to length and length to width of the magazine photograph are 2:3 and 3:2 respectively.

Explanation:

The question is asking for the ratios relating to the dimensions of the magazine photograph. In this case, the photo is 24 cm long and 16 cm wide. Therefore, you can derive various ratios from this.

The first is the ratio of width to length, which is 16 : 24. This can be simplified by finding the highest common factor of 16 and 24, which is 8. So divide both sides of the ratio by 8 to get 2 : 3.

Another ratio is the ratio of length to width, which is 24 : 16. Similarly, this can be simplified to a ratio of 3 : 2 by dividing both sides by 8.

Learn more about Ratios here:

https://brainly.com/question/32531170

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PLEASE WILL GIVE YOU BRAINY IF YOURRIGHT!!!!!!!!!!!!
What is the value of d?

−5.5(d−2)=−12.1

Enter your answer in the box.

Answers

d=4.2

-5.5(d-2)=-12.1
distribute
-5.5d+11=-12.1
subtract 11 from both sides
-5.5d=-23.1
divide -5.5 on both sides
d=4.2

Answer:

4.2

Step-by-step explanation:

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