Two athletes practice for a marathon by running back and forth on an 11-mile course. They start running simultaneously, one at a speed 2 mph faster than the other's speed. How fast does each run if they meet 1 hour 6 minutes after starting? (The faster runner is already returning at this point.) How far from the starting point do the runners meet?

Answers

Answer 1

Answer:

Faster runner speed: 11 mph

Slower runner speed: 9 mph

Distance from starting point: 9.9 miles

Step-by-step explanation:

Let the slower runner speed be: x

Faster runner speed: x+2

1 hour 6 minutes = 1.1 hours

Slower: 1.1(x) = 1.1x miles

Faster: 1.1(x+2) = 1.1x+2.2 miles

This means that the faster runner had gone 2.2 miles more than the slower runner.

1.1x + 2.2 > 11 miles (This is true as we know the faster runner is coming back from the 11 mile run)

1.1x > 11 - 2.2 miles

1.1x > 8.8 miles

x > 8.8 / 2.2 miles

x > 8 mph

1.1x < 11 miles (we know this is true as the slower runner has to have gone less than 11 miles as the faster runner met him on his way back)

x < 11 / 1.1 miles

x < 10 miles

8 < x < 10

Although x could be any number including decimal between 8 and 10, the obvious first answer would be 9. However we need to check if this answer is correct.

Slower runner distance to the end:

1.1(9) = 9.9 miles

11 - 9.9 = 1.1 miles

Faster runners distance from the end (when coming back)

1.1(9+2) = 1.1(11) = 12.1 miles

12.1 - 11 = 1.1 miles

The speeds 9 mph and 11 mph are now proven to be the right speeds. Using our equation before, we can figure out the distance from the starting point that they meet at. This is just how far the slower runner has gotten. So, 1.1(9) = 9.9 miles from the starting point


Related Questions

A shoe store uses a 60​% markup for all of the shoes it sells. What would be the selling price of a pair of shoes that has a wholesale cost of ​$55​?

Answers

The selling price should be $88

Given that,

The markup percentage is 60% and the wholesale cost is $55.

calculation:

= $55 + (60% of $55)

= $55 + $33

= $88

Learn more about the price here: https://brainly.com/question/25300841?referrer=searchResults

Answer:

88

Step-by-step explanation:


Solve the equation for x.

4x = 32
A) x =
1
8
B) x = 8
C) x = 28
D) x = 36

Answers

Answer:

B) x = 8

Step-by-step explanation:

4x = 32

4x/4 = 32/4

x = 8

I hope this helps! May I have brainliest pls? :)

The answer is B because you divide 32 by 4

2x + 3y = 53
3x - y = 19
Work out the values of x and y.

Answers

Answer:

y = 11

x = 10

See pictures for how to do it and ask me if you still dont understand

The following expression represents the profit made by John as he mows lawns: P = 20L
- 100
Which description correctly interprets each part of the expression?

Answers

its c because i already did that and got it right

At high tide, the bay is at 10 feet. As the tide recedes it is now at 8 feet. What is the percent change

Answers

If I'm correct the answer would be 8.


Consider the pyramid below:
12 cm
15 cm
What is the length of a ?

Answers

[surface area of the square pyramid]=area of the base+4*[area of one lateral triangle]

area of the base=12²----> 144 cm²

area of one lateral triangle=b*h/2
b=12 cm
h=slant height -----> 15 cm
area of one lateral triangle=12*15/2-----> 90 cm²

[surface area of the square pyramid]=144+4*[90]----> 504 cm²

the answer is
the surface area of the square pyramid is 504 cm²

Write the ratio 42:24 in its simplest form.

Answers

Answer:

7:4

Step-by-step explanation:

42:24

divide both sides by 6

7:4

Answer:

Find the GCD (or HCF) of numerator and denominator. GCD of 42 and 24 is 6.

42 ÷ 624 ÷ 6.

Reduced fraction: 74. Therefore, 42/24 simplified to lowest terms is 7/4.

Step-by-step explanation:

Do the fractions in the table convert to repeating or terminating decimals in each row of the table select either repeating decimal or terminating decimal as your answer

Answers

2/9 has a repeating decimal

3/25 has a terminating decimal

7/40 has a terminating decimal

5/11 has a repeating decimal

4/5 has a terminating decimal

Hope this helped! :)

The average annual salary for a teacher national is $58,350 this is projected to increase 2% per year for the next four years what will your projected annual salary be in four years

Answers

Answer:

Step-by-step explanation:

[tex]F=Ir^t,\text{ where F=final amount, I=initial amount, r=rate of change, t=time}\\ \\ F=58350(1.02)^4\\ \\ F=\$ 63159.92[/tex]

please help giving lot of points

Answers

Answer:

They would need to sell 32 calendars to EXCEED their goal.

Explanation:

8 x 32= 256, which is more than the $250 needed!

Step-by-step explanation:

8x32=256 which is a lot more than needed

Two expressions are shown below. Explain whether or not expressions P and Q are equivalent.
P: 2(3x –9)
Q: 6x –9

Answers

Answer:

Not equivalent

Step-by-step explanation:

So basically when it says 2(3x-9) to simplify you need to remove the parentheses so the 2 multiplies both like this; 2×3x + 2×-9= 6x-18

So, 6x-9 is not equal to 6x-18

Answer:

It wouldnt be equivalent

for P, you have to do distributive property.

2×3x equals 6 and then you times 2×-9 which is -18. P= 6x-18. Therefore, it is not equivalent.

The scatter plot shows the number of hours of sleep each night and the number of hours of television watched. Use the scatter plot to complete this statement: A person who watches ________ hours of television would expect to get 12 hours of sleep.

Answers

Answer:

It's 1

Step-by-step explanation:

The x axis is the "Hours of Sleep Each Night"

Look at 12 on the x coordinate

Look at y axis

You then see that A person who watches ____1____ hours of television would expect to get 12 hours of sleep.

Answer:

its 1 because i already had TTM with Mrs.Kajmowics and Mrs.Ortiz

Step-by-step explanation:

4. Which of the following equations represent
linear function?
O A. y = 3x2
6
B. y = 2
C. y=V x + 6
D. y= }++3
Help fast pls

Answers

Answer:

Can you take picture, please?

What is the value of 6x - 3y if x = 5 and y = 1

Answers

Answer:

6x-3y

6(5)-3(-1)

30+3

The answer is 33

Step-by-step explanation:

Brainliest please :)

answer: 27

6×5-3×1

30-3=27

solve each proportion algebraically. show your work. n/6 = 25/30​

Answers

i’m pretty sure the answer is n=5

HELP ASAP Four times the quotient of 3 and 4.

Answers

Answer:

it is 4

Step-by-step explanation:

all you do is multipla

(x^b-c)^1÷bc×(x^c-a)^1÷ac×(x^a-b)^1÷ab​

Answers

Hope this helps (sorry if u cant see that)

why wealthy colonists used the Africans as workers? help asp ​

Answers

Answer:

they provided cheap labour

Step-by-step explanation:

this is because Africans were sold as slaves to the rich colonialists.

"Y varies directly as x". If y = 3 when x = 24, find y when x = 10.

Answers

Answer:

y=3x-24

Step-by-step explanation:

help please mathematics​

Answers

This equation is subtracting 1/4 at a time. The next three numbers would be 3, 2 3/4, and 2 1/2.

HELP!!!ITS DUE IN AN HOUR
A salesperson at a jewelry store earns 5% commission each week. Last week, Heidi sold $530
worth of jewelry. How much did she make in commission? How much did the jewelry store make
from her sales?
Heidi earned in commission.

Answers

Answer:

26.5

Step-by-step explanation:

dont worry I'm actually the salesperson at the  jewlery store

Step-by-step explanation:

it is not confrmed answer

commission:106%

the photo says it all

Answers

y=8, hope this helps

What is the value of the expression shown? 24-5^2

Answers

Answer: -1

Step-by-step explanation:

Order of Operations, 5 to the power of 2 is 25 24-25 is -1 Hope this helps!

Answer:

-1

Step-by-step explanation:

24 - 5^2

24-25

=25-24

= -1

define oayday lenders​

Answers

Short term and low value,high interest cash loaners

Isaiah scores with 50% of his penalty kicks in soccer. He flips two fair coins to conduct a simulation with 20 trials to determine the likelihood that he will make his next two penalty kicks, as shown. Heads up (H) represents a goal. What is the probability that Isaiah will make both penalty
TH HH TT HT
TH HH HH TT
HT TH TT HH
HT HH HH TT
HT HH TH TT

P(two goals) kicks? Give the probability as a percent. Enter your answer in the box.

Answers

Answer:

35%

Step-by-step explanation:

He made 7 out of 20 goals

7/20=0.35=35%

The probability as a percentage is  20%.

What is probability?

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

Out of the five Trials,

We can see that only one of them has Isaiah making both penalty kicks (TH HH HH TT).

Therefore, the probability that Isaiah makes both penalty kicks is 1/5 or 0.2.

Converting to a percentage,

0.2 x 100

= 20%

The probability is 20%.

Thus,

The probability as a percentage is  20%.

Learn more about probability here:

https://brainly.com/question/14099682

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Given m<2 = 55°, find the measure of each missing angle.

Answers

Answer:

1. m<1 = 125°

2. m<4 = 125°

3. m<6 = 55°

4. m<8 = 125°

Step-by-step explanation:

1. 180 - 55 = 125

2. 180 - 55 = 125

3. m<2 = m<6 , m<6 = 55°

4. m<4 = m<8 , m<8 = 125°

The sum of eight times a number and negative exceeds twelve.

Answers

Answer:8x + -4 > 12

8x > 16

x > 2

Step-by-step explanation:

6. For a trip to the beach, Kelly drove for 5/6 hour and Joshua drove for 2/5 hour. How much longer did Kelly drive than Joshua? Find the exact amount.​

Answers

first find common denominator, i went with 30. multiply the numerators, they should be 12/30 and 25/30. now just subtract 25/30-12/30 which gives us 13/30.
ANSWER: 13/30 or 26 minute difference

The number of hours Kelly drove longer than Joshua is 13/30 hours.

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

The number of hours driven by Kelly.

= 5/6 hours

The number of hours driven by Joshua.

= 2/5 hours

Now,

The difference between the number of hours driven by Kelly and Joshua.

= 5/6 - 2/5

= (25 - 12)/30

= 13/30

Thus,

Kelly drove 13/30 hours longer.

Learn more about fractions here:

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What is the quotient in simplest form?
12/7 divided by 3

Answers

Answer:

your answer would be 4/7.

Step-by-step explanation:

divide the 12 by 3 giving 4 ... 4/7

$750 loan 7% a year three years of no payments how much interest are you paying?

Answers

Answer:

$157.50

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 7%/100 = 0.07 per year,

then, solving our equation

I = 750 × 0.07 × 3 = 157.5

I = $ 157.50

The simple interest accumulated

on a principal of $ 750.00

at a rate of 7% per year

for 3 years is $ 157.50.

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