5

An athlete covers three consecutive miles by walking the first mile, running the second mile

and cycling the third. He runs twice as fast as he walks, and he cycles one and a half times as

ast as he runs. He takes ten minutes longer than he would do if he cycled the three miles,

How long does he take by walking, running and cycling?

ter your math answer

Answers

Answer 1

Answer:

Total time taken by walking, running and cycling = 22 minutes.

Step-by-step explanation:

Let the speed of walking = x

As given,

The distance of walking = 1

Now,

As [tex]Time = \frac{Distance }{Speed}[/tex]

⇒ Time traveled by walking = [tex]\frac{1}{x}[/tex]

Now,

Given that - He runs twice as fast as he walks

⇒Speed of running = 2x

Also given distance traveled by running = 1

Time traveled by running = [tex]\frac{1}{2x}[/tex]

Now,

Given that - he cycles one and a half times as  fast as he runs.

⇒Speed of cycling =  [tex]\frac{3}{2}[/tex] (2x) = 3x

Also given distance traveled by cycling = 1

Time traveled by cycling = [tex]\frac{1}{3x}[/tex]

Now,

Total time traveled = Time traveled by walking + running + cycling

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

                                = [tex]\frac{6+3+2}{6x} = \frac{11}{6x}[/tex]

If he cycled the three mile , then total time taken = [tex]\frac{1}{3x}[/tex] + [tex]\frac{1}{3x}[/tex] + [tex]\frac{1}{3x}[/tex] = x

Given,

He takes ten minutes longer than he would do if he cycled the three miles

⇒x + 10 = [tex]\frac{11}{6} x[/tex]

⇒[tex]x - \frac{11}{6} x = -10[/tex]

⇒[tex]-\frac{5}{6}x = -10[/tex]

⇒x = [tex]\frac{60}{5}[/tex] = 12

⇒x = 12

∴ we get

Total time traveled by walking + running + cycling = [tex]\frac{11}{6} x = \frac{11}{6} (12) = 11 (2) = 22[/tex] min


Related Questions

you have one sheet of 18 stickers. If you put an equal amount of stickers on 3 sheets of paper, how many stickers will be on each page?

Answers

Answer

there will be 6 on all three pages

Step-by-step explanation:

divide 18 by 3

Find the distance between (-5,6)and (3,2).

Answers

Answer:

[tex]\displaystyle d = 4\sqrt{5}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Coordinates (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 (-5, 6) → x₁ = -5, y₁ = 6

Point (3, 2) → x₂ = 3, y₂ = 2

Step 2: Find distance d

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

Substitute in points [Distance Formulas]:                                                     [tex]\displaystyle d = \sqrt{(3+5)^2+(2-6)^2}[/tex][Distance] [√Radical] (Parenthesis) Add/Subtract:                                       [tex]\displaystyle d = \sqrt{(8)^2+(-4)^2}[/tex][Distance] [√Radical] Evaluate exponents:                                                    [tex]\displaystyle d = \sqrt{64+16}[/tex][Distance] [√Radical] Add:                                                                             [tex]\displaystyle d = \sqrt{80}[/tex][Distance] [√Radical] Simplify:                                                                         [tex]\displaystyle d = 4\sqrt{5}[/tex]

An inequality is like an equation, but instead of an equal sign (=) it has one of these signs: ______________, _______________ , ________________, _____________.

Answers

Answer:

An inequality sign is like an equal sign with a line through it

so, like, if you put = and / together

Answer:

<, >, =>, =<

Step-by-step explanation:

Algebra 2 Unit 1 Assessment
Which of the following contains multiple variables?
4a + 5b + 1

4a + 5a + 1

4a - 1

4 - 1

Answers

Answer:

I would have to say A

Step-by-step explanation:

B has 2 of the same variables while A has to different variables and C&D have no variables there for the answer is A

i also think it’s A

Simplify completely*****​

Answers

Answer:

[tex]\displaystyle x - 3[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Terms/CoefficientsFactoring

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \frac{x^2 + 7x - 30}{x + 10}[/tex]

Step 2: Simplify

[Fraction] Factor numerator:                                                                           [tex]\displaystyle \frac{(x - 3)(x + 10)}{x + 10}[/tex][Fraction] Divide:                                                                                             [tex]\displaystyle x - 3[/tex]

For which value of x must the expression V59X be further simplified?

Answers

R t tvyvyvy t y. Hcyctvyvvyvubi

5у2 2is a power + бу - 4

Answers

Answer:

Its 5000

Step-by-step explanation 4883-3455=5000

[tex](4+\sqrt{-7}) (3+\sqrt{-7})[/tex]

Answers

HMMMMMMMMMM LET ME WORK IT OUT FOR U
The answer is 5+7i√7

What is 56x1
Just a regular normal question from me
Your welcome in advance

Answers

Answer:

56

Step-by-step explanation:

Hope this helps

Answer:

56

Step-by-step explanation:

56×1=56

Which graph represents the function?

f(x)=x+2‾‾‾‾‾√3

Answers

Answer:

the correct answer is the last one to the right side

Answer:

Equation :

f(x) = ³√x+2

The fourth option.

See image.

I hope the image helps.

PLZ HELP
x-5(x-1) = x- (2x-3)​

Answers

Answer:

Step-by-step explanation:

x-5(x-1) = x- (2x-3)​

x  + x *(-5) + (-1) * (-5) = x +  2x*(-1) + (-3)*(-1) {use distributive property}

x - 5x + 5 = x - 2x +3   {Combine like terms}

    -4x + 5 = - x +3           {Add 'x' to both sides}

-4x + 5 + x  = -x + x + 3

       -3x + 5 = 3           {subtract 5 from both sides}

            -3x = 3 - 5

            -3x = -2           {Divide both sides by (-3)}

              x = -2/-3

               x = 2/3

can you help me solve this plz?

Answers

Answer:

x=5.6  y=4.8

Step-by-step explanation:

The answer is X=5.6 y= 4.8

The sum of 3 and
twice the number n

Answers

3x2= 6 so it’s 6 which is equal to n

Reasoning : The equation below describes a proportional relationship between x and y. What is the
constant of proportionality? Use pencil and paper. Explain why your answer is called the "constant of
proportionality."
y = 7.87x

Answers

Answer:

The constant of  proportionality is 7.87.

Step-by-step explanation:

The relation between x and y is given by the equation :

y = 7.87x

y is directly proportional to x i.e.

y ∝ x

To remove the constant of proportionality, a constant 7.87 is inserted. Hence, the constant of  proportionality is 7.87.

Prove that
sinAtanA/1-cosA
= 1 + SECA

Answers

Answer:

The proof is done in the step-by-step explanation below.

Step-by-step explanation:

We are given the following identity:

[tex]\frac{\sin{A}\tan{A}}{1-\cos{A}}[/tex]

And we have to show that this is equals to:

[tex]1 + \sec{A}[/tex]

Multiplying numerator and denominator by the conjugate of the denominator:

[tex]\frac{\sin{A}\tan{A}}{1-\cos{A}} \times \frac{1+\cos{A}}{1+\cos{A}}[/tex]

[tex]\frac{\sin{A}\tan{A}(1+\cos{A})}{1 - \cos^2{A}}[/tex]

We use these following identities:

[tex]\sin^2{A} + \cos^2{A} = 1[/tex]

So

[tex]1 - \cos^2{A} = \sin^2{A}[/tex]

Also:

[tex]\tan{A} = \frac{\sin{A}}{\cos{A}}[/tex]

Then

[tex]\frac{\sin{A}\sin{A}(1+\cos{A})}{\cos{A}\sin^2{A}}[/tex]

[tex]\frac{\sin^2{A}(1+\cos{A})}{\cos{A}\sin^2{A}}[/tex]

[tex]\frac{1 + \cos{A}}{\cos{A}}[/tex]

[tex]\frac{1}{\cos{A}} + \frac{\cos{A}}{\cos{A}}[/tex]

[tex]\frac{1}{\cos{A}} + 1[/tex]

Since:

[tex]\sec{A} = \frac{1}{\cos{A}}[/tex]

We have that:

[tex]1 + \sec{A}[/tex]

Thus, the proof is done.

11). Miguel has $87,255 in a savings account that earns 9% interest per year in simple interest. To the nearest cent, how much will he have in 4 years? OA). $31,411.80 O B). $123,167.55 O C). $35,912.55 OD). $118,666.80​

Answers

Answer:

[tex]A). \: \$31,411.80[/tex]

Step-by-step explanation:

[tex]s.i = \frac{p \times r \times t }{100} \\ \\ s.i = \frac{87255 \times 9 \times 4}{100} = 31,411.8[/tex]

Answer:A

Step-by-step explanation:

when a two digit number is multiplied by its unit digits, the product is 336. When the digits are reversed and the new number is multiplied by its new unit digits, the product is 325.If the sum of the digits is 11, find the original two digit number​

Answers

9514 1404 393

Answer:

  56

Step-by-step explanation:

In the base-10 number system, the only two digits that have themselves as the least significant digit of their square are 5 and 6.* If multiplying a 2-digit number by the ones digit gives a ones-digit of 6, then the ones digit must be 6.

Similarly, if the ones digit of the product is 5, the ones digit of the number must be 5.

So, the ones digit of the original number is 6, and the ones digit of the reversed 2-digit number is 5. The original number is 56.

__

Check

  56 × 6 = 336

  65 × 5 = 325

  5 + 6 = 11

_____

* Additional comment

These digits are called "automorphs." Automorphs ending in 5 or 6 can be extended to any number of digits. For example, the 3-digit automorph ending in 6 is 376. 376² = 141376. Similarly, the 3-digit automorph ending in 5 is 625. 625² = 390625

1. (-78) + (-98) =
2. (+45) + (+23) =
3. (+67) + (-56) =
4. (98) + (-73) =
5. (-971) + (+237) =​

Answers

Answer:

1.-179

2.68

3. 11

4. 25

5. -734

A beverage manufacturer performs a taste-test and discovers that people like their fizzy beverages best when the radius of the bubbles is about 0.3 mm. According to the formula below, what would be the volume of one of these bubbles? r = root(3, (3V)/(4s))​

Answers

v= 4πr³ / 3

V = 4(3.14) (0.3)³ / 3

V = 0.11 mm³

Option A
The volume would be answer A.

Alicia bought a package of eight peaches for $3.20. Find the cost of each peach.

Answers

Answer:

.40 cents each.

Step-by-step explanation:

$3.20/8=.40

Question 11
Rhonda deposits $5,600 in a savings account that pays 1.36% Interest, compounded semiannually. What is the balance after the first 9 months?

Answers

Answer:

follow me please and give thanks

Marla mixed cream and milk in a ratio of
2 parts cream to 3 parts milk. How many
liters of each did she use if she made 20 liters

Answers

Answer:

If it says she made 20 liters of cream then She has 30 liters of milk

Step-by-step explanation:

2 cream x 10 = 20

3 milk x 10 = 30

Hope this helps!

Plz make me Brainliest.

A state began an effort to increase the deer population. In year 2 of the effort, the deer population in a state forest was 3,000. In year 4, the population was 4,320.

The explicit rule for the geometric sequence is aₙ =

Answers

Step-by-step explanation:

i guess math is the hardest subject

Answer:

The answer is aₙ = 2,500 (6/5)^n-1

Hope i helped, have a wonderful day! :D

The scale factor of similar figures is 4/3, and one side of the smaller triangle is 12.

The corresponding side on the larger triangle is 16.

True
False

Answers

Answer:

True

Step-by-step explanation:

The solid contains a cylinder and a hemisphere. Find the volume of the composite solid. 4.4m radius and 5m height

Answers

Answer:

303.95 m^3

Step-by-step explanation:

Volume = πr2h

r= 4.4

h = 5

= 3.14 × 4.4^2 × 5

= 3.14 × 19.36 × 5

= 303.95

Hence the volume is 303.95 m^3

Question :-

The solid contains a cylinder and a hemisphere. Find the volume of the composite solid that has a radius of 4.4 m and a height of 5 m.

Answer :-

The volume of the composite solid is 303.952 m³.

[tex] \rule{180pt}{4pt}[/tex]

Diagram :-

[tex]\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{4.4 \: m}}\put(9,17.5){\sf{5 \: m}}\end{picture}[/tex]

Solution :-

As per provided information in the given question, we have been given that the Radius of a cylinder is 4.4 meters. The height of a cylinder is 5 meters. We have been asked to find the volume of a cylinder.

To calculate the volume of a cylinder, we will apply the formula below :-

[tex] \bigstar \: \: \: \boxed{ \sf{ \: \: Volume_{(Cylinder)} = \pi r^2 h \: \: }}[/tex]

Substitute the given values into the above formula and solve for Volume :-

[tex]\sf:\implies Volume_{(Cylinder)} = \pi r^2 h[/tex]

[tex]\sf:\implies Volume_{(Cylinder)} = (3.14)(4.4 \: m)^2(5 \: m)[/tex]

[tex]\sf:\implies Volume_{(Cylinder)} = (3.14)(19.36 \:m^2)(5 \: m)[/tex]

[tex]\sf:\implies Volume_{(Cylinder)} = (60.7904 \:m^2)(5 \:m)[/tex]

[tex]\sf:\implies\bold{Volume_{(Cylinder)} = 303.952 \: m^3}[/tex]

Therefore :-

The volume of the composite solid is 303.952 m³.

[tex]\\[/tex]

Learn more about the Volume of a Cylinder at https://brainly.com/question/15197979

Have a great day! <33

Which of the following are exterior angles? Check all that apply

Answers

Answer: D, C, A

Step-by-step explanation:

An exterior angle is an angle that is supplementary to an interior angle.

The angle between the extended side and its adjacent side is called the exterior angle so the option (D), (C), and (A) will be the correct answers.

What is the Exterior angle?

Exterior angles become by a side of that figure and its extended adjacent side.

The exterior angle has been attached.

Since in the graph angle, ∠3 become by two extended lines but for exterior angle, there should be only one extended line which is ∠6, ∠5, and ∠2.

Hence angles ∠6, ∠5, and ∠2 will be the exterior angles.

For more information about Exterior angle

https://brainly.com/question/10638383

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Quadrilateral WXYZ is dilated by a scale factor of į to form quadrilateral W'X'Y'Z'. What is the measure of side ZW? Z 28 Y" 42 42 W 28​

Answers

Answer:

See Explanation

Step-by-step explanation:

Given

The given side lengths are not clear enough:

So, I will give a general explanation.

From the question, we understand WXYZ is dilated to produce W'X'Y'Z

This implies that the sides of WYZY is multiplied by the scale factor (k) to give W'X'Y'Z'

i.e.

[tex]ZW *k =Z'W'[/tex]

Divide both sides by k to get side length ZW

[tex]ZW = \frac{Z'W'}{k}[/tex]

Assume that:

[tex]k = 4[/tex] and

[tex]Z'W' = 28[/tex]

[tex]ZW = \frac{Z'W'}{k}[/tex]

[tex]ZW = \frac{28}{4}[/tex]

[tex]ZW = 7[/tex]

Apply these steps and you will get your answer

Find the length of the third side. If necessary, write in simplest radical form.
3
2

Answers

Answer:

4.2 ft

Step-by-step explanation:

Reference angle = 77°

Opposite side = DE = x

Hypotenuse = CD = 4.3 ft

Apply the trigonometric function of sine. Thus:

Sin 77 = opp/hyp

Sin 77 = x/4.3

Multiply both sides by 4.3

4.3 × sin 77 = x

x = 4.2 ft (nearest tenth)

Is 13:15 and 30:26 a pair of equivalent ratios and why?

Answers

Given:

The two ratios are 13:15 and 30:26.

To find:

Whether the given ratios are equivalent or not.

Solution:

Two ratios are equivalent if the values of the ratio are equal after simplification.

[tex]13:15=\dfrac{13}{15}[/tex]

And,

[tex]30:26=\dfrac{30}{26}[/tex]

[tex]30:26=\dfrac{15}{13}[/tex]

[tex]30:26=15:13[/tex]

The first ratio is 13:15 and the value of second ratio after simplification is 15:13 both ratios are different, so,

[tex]\dfrac{13}{15}\neq \dfrac{30}{26}[/tex]

Therefore, the required answer is "No", the given ratios are not a pair of equivalent ratios.

A circle has a central angle of 6 radians that intersects an arc of length 14in

Answers

c=2pir

arclength/circumference=centralangle/2piradians

14/2pir=6/2pi
7/pir=3/pi
times pir both sides
7=3r
divide by 3 both sides
7/3=r

well,
um
the answer is B
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