A tortoise and a hare are competing in a race around a 1600-meter track. The arrogant hare decides to let the tortoise have a 780-meter head start. When the start gun is fired the hare begins running at a constant speed of 10 meters per second and the tortoise begins crawling at a constant speed of 5.3 meters per second.

Answers

Answer 1

I am presuming that the question is who won or by how much did the winner win.

distance equals rate times time, or d = r*t
For the Hare d = 1600 and r = 10
1600 = 10 t
Divide both sides by 10
t = 160
The hare finished in 160 seconds

For the tortoise d = 1600 - 780 = 820 (due to the head start) and r = 5.3
820= 5.3 t
Divide both sides by 5.3
t = 154.72 (rounded to the hundredths place)

The tortoise won by 5. 28 seconds (160-154.72)

Answer 2

The tortoise wins. The tortoise takes 154.7 seconds to finish the race. The hare takes 160 seconds to finish the race. There really isn't a question here, but I'm going to assume the unasked question is one of "Who wins?" "How long does it take the tortoise to complete the race?" or "How long does it take the hare to complete the race?" And thankfully, in determining the answer to "Who wins?" will have as a side effect the answers to the other two questions. First, how many seconds does it take for the hare to complete the race. Just divide the distance by the speed and you'll have the answer. So 1600 m / 10 m/s = 160 s Now, how many seconds does it take the tortoise to finish the race? Same thing. Distance divided by speed. But there's a twist, you need to figure out the distance. And that is just the track length minus the head start. So (1600 m - 780 m) / 5.3 m/s = 820 m / 5.3 m/s = 154.717 s And since the tortoise took less time than the hare, the tortoise wins.

Related Questions

You are paid $82.50 for 7 1/2 hours of work. What is your rate of pay?

Answers

$82.50/7.5= $11 dollars an hour

all you have to do is take the total, and divide it by how long you work, in order to get how much you made per hour.

hope this helped!

Rate of pay is 11 dollars

Using the speaking outline, how many times should you practice? five or more three two one

Answers

According to the speaking outline, it is recommended to practice your speech at least five times or more.

According to the speaking outline, you should practice your speech "five or more" times. Practicing your speech multiple times helps you become more familiar with the content, improve your delivery, and gain confidence in your presentation. The more you practice, the better prepared you'll be to deliver a successful speech.

Therefore, it is recommended to practice your speech at least five times or more.

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According to the speaking outline, it is recommended to practice your speech at least five times or more.

According to the speaking outline, you should practice your speech "five or more" times.

Practicing your speech multiple times helps you become more familiar with the content, improve your delivery, and gain confidence in your presentation.

The more you practice, the better prepared you'll be to deliver a successful speech.

Therefore, it is recommended to practice your speech at least five times or more.

for such more question on times

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Problem page the sum of two numbers is 56 . the smaller number is 16 less than the larger number. what are the numbers?

Answers

Create equations using the given information
1) x+y=56
2) y=x-16
Substitute the value of y into the 1st equation and simplify
1)x+x-16=56
2x=72
x=36
Substitute the value of x into the 1st equation and simplify
1)x+y=56
36+y=56
y=20

Answer: 20 and 36

Given B = {a, l, g, e, b, r} and C = {m, y, t, h}, find B ∪ C

Answers

The union of two sets includes elements found in both sets. Here, including every element in both B and C yields the set B ∪ C = {a, l, g, e, b, r, m, y, t, h}

if x^2+14x-95=(x+a)(x+b), then the numerical value for ab is

Answers

x^2+14x-95 = (x+19)(x - 5)

a = -5
b = 19

Susan can run 2 city blocks per minute. she wants to run 60 blocks. how long will it take get to finish if she has already run 18 blocks?

Answers

Im pretty sure the answer is 12

Kristin is 20 miles behind a truck that is driving 50 miles per hour. How long will it take her to catch up to the truck? How far will she go in that time

Answers

t = 20/(r-50)t=20/r-50 hours

Final answer:

It will take Kristin 24 minutes to catch up to the truck. She will travel a distance of 20 miles in that time.

Explanation:

To calculate how long it will take for Kristin to catch up to the truck, we can use the equation: time = distance / speed. Since Kristin is 20 miles behind the truck, she will need to cover a distance of 20 miles to catch up to the truck. Assuming she drives at a constant speed, we can use her speed as the truck's speed since she needs to match it to catch up.

Time to catch up = 20 miles / 50 miles per hour = 0.4 hours = 24 minutes.

In that time, Kristin will travel the same distance as the truck. So, she will go 20 miles in 24 minutes.

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Find the simple interest on a loan of $3,500 at 7.8% interest for 9 months

Answers

3,500 + (3,500 7.8)*9

If you're going 80 miles per hour how long does it take to go 80 miles answer

Answers

an hour cause u go 80 per HOUR

Find h(-1), h(0), and h(4) for the given function h(x)=-2x^2-4

Answers

h=-2²-4
h(-1)=-2-4=-6
h(0)=-4
So there are twoo answers -6 and -4

How to find the measure of an exterior angle given the measure of the interior angle?

Answers

Exterior angles are always supplementary to the interior angle, because to get an exterior angle you have to keep the line going from one interior angle. That means that

(measure of interior angle)+(measure of exterior angle)=180 degrees

You can change the form of the equation and get

(measure of exterior angle)=180 degrees - (measure of interior angle)

So, to find the exterior angle, just subtract the interior angle from 180.

Hope this helps!

To convert 3.4 hours into seconds which two ratios could you multiply by

Answers

60 min/1 hr
60 sec/1 min

3.4 x 60 = 204 min
204 x 60 = 12240 seconds

12240 seconds is your answer

hope this helps

HELP ME PLEASE
Olga deposited $1500 in a savings account that pays 7.5% interest compounded quarterly. What is the balance in her account at the beginning of the third quarter?
A. $1,590
B. $1,560
C. $1,585.97
D. $1,591.81
ok let me make one thing clear: i have put up questions like this before but i am NOT TRYING TO JUST GET ANSWERS. I legit want to learn this. It is just hard for me i guess.. so sorry if this answer seems simple to you but its not to me so if you could please explain your answer CLEARLY, in particular with "compound quarterly." please explain so i can use the principles later on. Thank you!

Answers

Let P be the final value
Let r be the rate
Let t be the time in years
Let C be the initial value
Let n be the number of times interest is given per year

P = C (1 + r/n) ^ (nt)

r = 0.075 (7.5%)
t = 3/4 years
C = $1500
r = 4 (4 quarters in one year)

P = C (1+r/n)^ (t/n)
= 1500 * (1 + 0.075/4) ^ (3/4 * 4)
= 1585.97

Have an awesome day!

If you are wondering, a quarter means 1/4 of a year.

How many ways are there to distribute six different toys to three different children such that each child gets at least one toy?

Answers

give two toys to each child

which fraction is less than 7/15
A: 5/9
B: 6/11
C: 1/2
D: 4/9

Answers

Convert them all to decimals

The answer is D

D hope this helps
please give brainliest

If Tara spends $219 a month for her car payment and she makes $3200 a month what percent of her monthly income is spent on her car payment

Answers

The percent is calculated as the ratio of the monthly paymen to the total income times 100.

Percent, % = ( [monthly car payment] / [ monthly income] ) * 100

% = ($ 219 / $ 3200) * 100 ≈ 6.8

Answer: approximately 6.8% of Tara's monthly income is spent of her car payment.

If you study hard, then you can pass the tests.
If you pass the tests, then you can pass the class.

What conclusion can be draw from the statements above?
A) Studying hard will allow you to pass the class.
B) Only students who pass tests study hard.
C) If you have passed the class, you must not have studied very hard.
D) Not passing tests means that you did not study.

Answers

I think we all know it's A XD

Answer:

A) Studying hard will allow you to pass the class.

Katherine owns the trendy boutique where Clara works as a shop assistant. Deanne loves the clothes in Katherine's boutique and shops there often. Which of these three people is a consumer?

Answers

Deanne is the consumer

Answer:

Deanne

Step-by-step explanation:

Deanne is a consumer

A student has selected 8 books that she likes, but she has money only for 3 books. how many possible selections does she have?

Answers

Since the order of the books chosen doesn't matter, we use the combination formula to find the number of possible selections. Recall that a combination of k items from a set of n items is given by [tex]nCk= \frac{n!}{k!(n-k)!} [/tex].

In this problem, n = 8 and k = 3. So the number of possible selections is
[tex]8C3= \frac{8!}{3!(8-3)!}=56 [/tex]. Thus the answer is 56.

The student has 6,720 selections to choose from. Because order doesnâ€™t matter, the problem is a combinations function. It is solved by dividing the factorial of 8 by the factorial of 3. So (8*7*6*5*4*3*2*1)/(3*2*1)

If one candy bar weighs 3 ounces what is the weight of 11 candy bars

Answers

Final answer:

The weight of 11 candy bars is calculated by multiplying the weight of one candy bar, which is 3 ounces, by 11. The total weight for 11 candies is equal to 33 ounces.

Explanation:

If one candy bar weighs 3 ounces, the weight of 11 candy bars can be found by multiplying the weight of one candy bar by the number of candy bars. The calculation would be as follows:

Multiply the weight of one candy bar by the number of candy bars: 3 ounces × 11 = 33 ounces.

Therefore, the weight of 11 candy bars is equal to 33 ounces.

A car travels 83 7/10 miles on 2 1/4 gallons of fuel. Which is the best estimate of the number of miles the car travels on one gallon of fuel

Answers

round miles up to 84

round gallons down to 2

and divide

84 /2 = 42 miles per gallon ( estimate)

I need help finding v

Answers

check the picture below.

surely you can solve for "v", right?

A train fare costs £23.55
All train fares are increased by 2.8%

Work out the new fare.
[2 marks]

Answer.......

4 A savings account pays 3.6% per annum simple interest.
Heidi puts £400 into the account.

How much will she have in the account after 5 years?
[2 marks]

Answer .............

5 In one week the mass of a puppy increases from 1.8 kg to 2.25 kg

Work out the percentage increase of the mass.
[2 marks]

Answer............

Answers

1)
23.55+23.55×0.028
=24.21

2)
The formula is
A=p (1+rt)
A future value?
P present value 400
R interest rate 0.036
T time 5years
A=400×(1+0.036×5)
A=472

3)
((2.25−1.8)÷1.8)×100=25%

Hope it helps!

Final answer:

To calculate an increase, multiply the original value by the percentage increase. For simple interest, use the formula Interest = Principal * Rate * Time. Percentage increase in mass can be found with the formula: [(Final mass - Initial mass) / Initial mass] * 100%. These methods result in a new train fare of £24.21, a bank balance after 5 years of £472, and a 25% increase in the puppy's mass.

Explanation:

1. To work out the new fare, we first need to calculate how much the fare has increased by. 2.8% of £23.55 is found by multiplying 23.55 by 0.028, which comes out to £0.66 (rounded to the nearest penny). Adding this increase to the original fare gives us a new fare of £24.21.

2. The simple interest can be calculated using the formula Interest = Principal * Rate * Time. In this case, Heidi's investment of £400 (the principal) is earning 3.6% (the rate) in interest every year for 5 years (the time). So, the interest Heidi earns equals £400 * 3.6% * 5 = £72. Adding this to the original amount gives us £472.

3. The percentage increase in the puppy's mass is calculated as follows: [(2.25 kg - 1.8 kg) / 1.8 kg] * 100%. So, the mass has increased by 25%.

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Angles A and B are complementary. If m/ A= 3x - 8 and m/ B = 5x + 10, whqt is the measure of each angle ? Show your work and explain the steps

Answers

Final Answer:

1. The measure of angle A is [tex]$22^\circ$.[/tex]

2. The measure of angle B is[tex]$68^\circ$.[/tex]

Explanation:

To find the measures of angles A and B, we can use the fact that they are complementary, meaning their measures add up to[tex]$90^\circ$.[/tex]Let's set up an equation using the given information:

[m_A + m_B = 90]

Given that[tex]$m_A = 3x - 8$[/tex]and (m_B = 5x + 10), substitute these expressions into the equation:

3x - 8 + 5x + 10 = 9

Combine like terms:

8x + 2 = 90

Subtract 2 from both sides:

8x = 88

Divide by 8:

x = 11

Now that we know the value of (x), we can find the measures of angles A and B:

[tex]\[m_A = 3x - 8 = 3(11) - 8 = 33 - 8 = 25\][/tex]

[tex]\[m_B = 5x + 10 = 5(11) + 10 = 55 + 10 = 65\][/tex]

Therefore, the measure of angle A is $25^\circ$ and the measure of angle B is [tex]$65^\circ$.[/tex] To check, we can verify that these angles are indeed complementary:

25 + 65 = 90

So, angles A and B satisfy the condition of being complementary.

Evaluate the expression when =m6 m2-18

Answers

So first, we should substitute the variable m for the value that we are given. If m=6, then plugging in 6 for m will give us the equation 6(2)-18. Then, we will get 12-18. After subtracting 18 from 12, we will get -6 as an answer.

PLEASE HELP!!!
1. The coordinates of the vertices of triangle ABC are A(-1,3), B(1,2) and C(-3,-1).

Determine the slope of each side of the triangle and use that information to determine if the triangle is a right triangle or not.

2.The coordinates of the vertices of quadrilateral JKLM are J(-3,2), K(4,-1), L(2,-5) and M(-5,-2).

Find the slope of each side of the quadrilateral and determine if the quadrilateral is a parallelogram

Answers

1. AB 3-2/-1-1
-1/2
BC 2+1/1+3
3/4
AC 3+1/-1+3
4/2=2
It is a right triangle

2. JK -1-2/4+3
-3/7
LM -2+5/-5-2
-3/7
KL -1+5/4-2
4/2=2
JM 2+2/-3+5
4/2=2
The quadrilateral is a parallelogram

what is 2.6 repeating as a fraction

Answers

2.6 repeating as a fraction would be 2 2/3

A 14.5-gallon gasoline tank is 3 — 4 full. how many gallons will it take to fi ll the tank?

Answers

Final answer:

It would take 3.625 gallons of gasoline to fill a 14.5-gallon tank that is already 3/4 full.

Explanation:

The question asks how many gallons of gasoline are needed to fill a 14.5-gallon tank that is already 3/4 full. To find the amount needed to fill the tank, we first determine how much gasoline is currently in the tank by multiplying 14.5 gallons by 3/4:

14.5 gallons × 3/4 = 10.875 gallons

This means that there are 10.875 gallons of gasoline in the tank at the moment. To find out how much more gasoline is needed to fill the tank, we subtract this amount from the tank's total capacity:

14.5 gallons - 10.875 gallons = 3.625 gallons

Therefore, it would take 3.625 gallons of gasoline to fill the tank.

\sqrt{6} + 3 \sqrt{6}

Answers

I think you mean the sqrt{6} + 3•sqrt{6}. If so, see attached picture.

In the set of real numbers, the first number less than -3 is -4.

True
False

Answers

Id Say True because -4 is less than -3 Because its going in negatives

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