Anthony travels 48 miles by car in the same time it takes him to travel 12 miles on his
bike. His average rate of speed by car is 24 miles per hour faster than his average rate of speed by bike. What is the average rate of speed for both the car and the bike?

Answers

Answer 1

Answer:

Anthony's average speed by car is 32 miles per hour and his average speed by bike is 8 miles per hour.

Step-by-step explanation:

Let the average rate (in miles per hour) at which Anthony travels by car be c and by bike be b.

His average rate of speed by car is 24 miles per hour faster than his average rate of speed on bike. In other words:

[tex]c = b + 24[/tex]

Anthony travels 48 miles by car in the same amount of time it takes him to travel 12 miles by bike.

Recall that distance is given by the rate multiplied by the time t.

Hence, c multiplied by time t equals 48 miles:

[tex]\displaystyle ct = 48[/tex]

Likewise, b multiplied by the same time t equals 12 miles:

[tex]bt = 12[/tex]

Solve. We can multiply the second equation by four:

[tex]4bt = 48[/tex]

Substitute:

[tex]ct = 4bt[/tex]

Divide:

[tex]c = 4b[/tex]

Since c = b + 24:

[tex](b + 24) = 4b[/tex]

Solve for b. Subtract:

[tex]24 = 3b[/tex]

And divide:

[tex]b = 8\text{ miles per hour}[/tex]

Hence, Anthony bikes at an average rate of 8 miles per hour.

Since his average speed by car is 24 miles per hour faster, his average speed by car is 32 miles per hour.

In conclusion, Anthony's average speed by car is 32 miles per hour and his average speed by bike is 8 miles per hour.


Related Questions

Pls help me with this.

Answers

Answer:

Step-by-step explanation:

Which graph represents a line with a slope of -1/2 and a y-intercept equal to that of the line y =2/3x – 2?

Answers

Step-by-step explanation:

I guess option 4 is the correct answer.

Four times the sum of two times X and six algebraic expression

Answers

Answer:

4(2x + 6)

Step-by-step explanation:

2 times x is 2x

The sum of 2 times x and 6 is 2x + 6

And we do 4 times that, making sure to put 2x + 6 in parentheses; we're multiplying 4 times the entire sum.

4(2x + 6)

y = 2/3x + 1

Solve for X and Y Intercept

Answers

Y intercept is 1 as it is the value output when X = 0 which can be solved simply by plugging 0 in for X and solving. The X Intercept is -1.5 as it is the value when Y=0 which can be solved by plugging 0 into the function for y and solving.

Answer:

x=(3/2,0)

y=   ( 0 , − 1 )

Step-by-step explanation:

Ajay is on the swim team. He improved his time on
the 50-yard freestyle from 32 seconds to 31 seconds.
What's the percent decrease in his time?
3.125%
3.23%
1.03%
3.2%

Answers

Answer: it should be  3.125%

Step-by-step explanation:

3.125% is the answer

What is the measure of ZW?

Select the best answer from the choices provided.
A.530
B. 74°
C.106°
D.116

Answers

Answer:

B) 74

Step-by-step explanation:

This is an icoseles triangle because of the 2 lines in each side. This makes <Y equal to <Z

Given:

<Y = <Z

All triangle angles add up to 180 so:

<W + <Y + <Z = 180

<W + 53 + 53 = 180

<W + 106 = 180

<W = 180 - 106

<W = 74

Label where the adjacent, hypotenuse and the opposite is on this triangle please :)

Answers

Answer:

Here you go

Step-by-step explanation:

12x15 in exponential notation

Answers

Answer:

5(6^2)

BRAINLIEST, PLEASE!

Step-by-step explanation:

12 x 15 = 180

180/5 = 36

=5(6^2)

What is the quotient of 5/6 and 3/8?

Answers

Answer:

2 2/9

Step-by-step explanation:

5/6 ➗3/8

We can use the reciprocal.

So, 5/6 * 8/3 = 40/18.

40/18 can be simplified to 20/9 or 2 2/9

Using the whole number 5, Define the additive inverse and the multiplicative inverse

Answers

Given : The whole number is 5.

Explanation

We use the whole number 5.

The additive inverse of 'a' is -a

a+(-a)=0

For the whole number 5, the additive inverse of 5 is -5

Multiplicative inverse of 'a' is [tex]\frac{1}{a}[/tex]

because [tex]a \cdot \frac{1}{a}=1[/tex]

So the multiplicative inverse of 5 is [tex]\frac{1}{5}[/tex]

Learn more :  brainly.in/question/9248396

Graph the line that passes through the points (-4,-6) and (-2,-7) and
determine the equation of the line.

Answers

Answer:

[tex]y=-\frac{1}{2}x-8[/tex]

Step-by-step explanation:

[tex](-4,-6)(-2,-7)[/tex]

Step 1. Find the slope (by using the slope-formula)

m = slope

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-7--6}{-2--4}[/tex]

[tex]m=\frac{-1}{2}[/tex]

[tex]m=-\frac{1}{2}[/tex]

Step 2. Create the equation of a line that has a slope of [tex]-\frac{1}{2}[/tex]

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

Step 3. Find the y-intercept

To do this, use any of the two points and substitute their x and y values

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

point: [tex](-2,-7)[/tex]

[tex](-7)=-\frac{1}{2}(-2)+b[/tex]

[tex](-7)=1+b[/tex]

[tex]b=-7-1[/tex]

[tex]b=-8[/tex]

Step 4. Write the equation in Slope-intercept form

[tex]y=mx+b[/tex]

[tex]y=-\frac{1}{2} x-8[/tex]

Simplify the expression: (-13.2) + 8.1

Answers

Step-by-step explanation:

(-13.2)+8.1

-13.2+8.2

Since, there are two signs i.e, '+' and '-' and the value of '-' is more

Therefore,

-5

I hope it helped U

I hope it helped Ustay safe stay happy

If y = 7,
Solve for x in 5y + 3x + 2y - 8x = -1

Answers

Step-by-step explanation:

Hi there!

Given; y= 7

5y + 3x + 2y - 8x = -1

Simply keep the value of y in the equation and simplify it;

5*7 + 3x -8x +2*7 = -1

35 - 5x +14 = -1

-5x = -1-49

X= -50/-5

Therefore, X= 10.

Hope it helps!

Hey there!

[tex]\textsf{5y + 3x + 2y - 8x = -1}[/tex]

➬ [tex]\textsf{7y - 5x = -1}[/tex]

➬ [tex]\textsf{7(7) - 5x = -1}[/tex]

➬ [tex]\textsf{49 - 5x = -1}[/tex]

➬ [tex]\textsf{ -5x + 49 = -1}[/tex]

[tex]\huge\boxed{{\bf SUBTRACT \ 49 \ to \ BOTH \ SIDES}}[/tex]

[tex]\textsf{-5x + 49 - 49 = -1 - 49}[/tex]

⇢ [tex]\textsf{CANCEL out: 49 - 49 because it gives you 0}[/tex]

⇢ [tex]\textsf{KEEP: -1 - 49 because it helps solve for your x-value}[/tex]

↱[tex]\textsf{-1 - 49 = -50}[/tex]↰

[tex]\huge\textsf{New EQUATION: \boxed{ \bf -5x = -50}}[/tex]

[tex]\huge\boxed{\textsf{\bf DIVIDE -5 to BOTH SIDES}}[/tex]

[tex]\mathsf{\dfrac{-5x}{-5}=\dfrac{-50}{-5}}[/tex]

⤳ [tex]\textsf{CANCEL out: } \mathsf{\dfrac{-5}{-5}} \textsf{ because it gives you 1}[/tex]

⤳ [tex]\textsf{KEEP: } \mathsf{\dfrac{-50}{-5}} \textsf{ because it helps you get the x-value}[/tex]

[tex]\huge\textsf{New EQUATION: \boxed{\bf x = \dfrac{-50}{-5}}}[/tex]

[tex]\mathsf{x = \dfrac{-50}{-5}}[/tex]

[tex]\mathsf{\dfrac{-50}{-5} = x }[/tex]

[tex]\huge\boxed{\bf SIMPLIFY \ ABOVE\ \& \ YOU\ HAVE}\\\huge\boxed{\bf YOUR\ RESULT \ OF\ THE \ X-VALUE}[/tex]

[tex]\mathsf{\dfrac{-50}{-10} = \bf 10}[/tex]

[tex]\huge\boxed{\textsf{Therefore, your answer is: x = 10}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The mean of 3 numbers is 7.two numbers are 4 and -5
Find the third number

Answers

Step-by-step explanation:

(-5+4+x)÷3=7

-5+4+x=21

x=21-4+5

x=22

l don't

know about this thing

R
5/3
S
Given right triangle QRS, what is the value of sin(30°)?
30°
5
V3
10
60°
o
o
V3
2
o

Answers

Answer:

1/2

Step-by-step explanation:

here ,

sin = p/h

or, sin (30⁰) = 5 /10

so sin (30⁰) = 1/2

The value of  sin(30°) given triangle QRS is; 1/2

Trigonometric Ratios

In trigonometric ratios, we know that;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

From the given triangle, we see that;

Opposite side to the angle 30° is 5 while hypotenuse is 10.

Thus;

sin 30° = 5/10

sin 30° = 1/2

Read more about trigonometric ratios at; https://brainly.com/question/13276558

HELP!! Use the properties of addition to simplify this expression. 6-8 +6f-2f​

Answers

Answer:

-2 + 4f

Step-by-step explanation:

6 - 8 + 6f - 2f​

2(3 - 4 + 3f -f)     [Distributive Property]

=> 2(-1 + 3f - f)

=> 2(-1 + 2f)

=> -2 + 4f

Answer:

4f-2

Step-by-step explan:

6-8+6f-2f

6-8+4f

4f-2

a triangle has a width of 4 cm and perimeter of 26 cm. find the length​

Answers

Answer:

9 ufh fcnbscbhbvxdfhbbhukkkocd

g(x) = 3x2 – 2x +7
2x + 5
Find g(-1)

Answers

Answer:

ans...g(-1) is 4 . Is it true?

g( ‐1 ) = 7

Step-by-step explanation:

substitute your (x) value with ( ‐ 1)

(4d−6d3+3d2)−(10d3+7d−2) find the difference

Answers

Answer: -16d³ + 3d² - 3d + 2

Step-by-step explanation:

Given expression

(4d - 6d³ + 3d²) - (10d³ + 7d - 2)

Expand parentheses

(REMEMBER to change [+, -] signs when there is a [-] sign in before)

=4d - 6d³ + 3d² - 10d³ - 7d + 2

Put like terms together

=-6d³ - 10d³ + 3d² + 4d - 7d + 2

Combine like terms

=(-6d³ - 10d³) + 3d² + (4d - 7d) + 2

=[tex]\boxed{-16d^3+3d^2-3d+2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

-16d³ + 3d² -3d + 2

Step-by-step explanation:

(4d−6d³+3d²) − (10d³+7d−2) =

-6d³ - 10d³ + 3d² + 4d - 7d + 2 =

-16d³ + 3d² -3d + 2

solve for y 7y-3y=8
plzzzz answer
will give brainliest!!!!

Answers

7y - 3y = 8
4y = 8
y = 8/4
y = 2
Hope this helps :)

Answer:

Step-by-step explanation:

7y-3y= 4y

4y=8

Here when its like this we need y by itself, so you take out 4 by dividing 8 by 4.

y= 2

18(p+5) in a verbal expression

Answers

Answer:

Five greater than a number,the result is multiplied by 18

The verbal expression for 18(p + 5) is eighteen times the quantity obtained by adding five to a number p.

The verbal expression for the algebraic expression 18(p + 5) can be described as "Eighteen times the quantity obtained by adding five to a value represented by 'p'." This expression represents a mathematical operation where a given value 'p' is increased by five, and then the result is multiplied by eighteen. This type of expression is commonly encountered in various real-world situations where a value needs to be adjusted and then scaled up by a certain factor. In this case, the result reflects the outcome of multiplying the adjusted value by eighteen.

To know more about  expression here

https://brainly.com/question/34132400

#SPJ3

hi can you help me ?​

Answers

Answer:

5,400

Step-by-step explanation:

do the exponent which is 10x10=100 then add it to 5,300

I need help with this please help me

Answers

here’s your answer;
a.f(2)
given,
f(x)=5x-6
now,put the value of x=2,then we have
f(2)=5*2-6
=10-6
f(2)=4.

plz help me in this question​

Answers

Answer:

Article 2 is less than Rs.26700.15617

8. A chair lift at a ski resort travels along the
cable as shown.
AY
6
4
O
U
w
w
2
t
0
0 2
4 6 8 10 12 14 16 18
1 unit = 10 ft
How long is the cable? Round your answer
to the nearest whole foot.

Answers

Answer:  187 feet

This value is approximate.

==========================================================

Explanation:

The cable is connected by these key points

A = (0,3)B = (6,5)C = (12,4)D = (18,2)

Let's use the distance formula to find the length of segment AB.

[tex]A = (x_1,y_1) = (0,3)\\\\B = (x_2,y_2) = (6,5)\\\\d = \text{Distance from A to B} = \text{length of segment AB}\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-6)^2 + (3-5)^2}\\\\d = \sqrt{(-6)^2 + (-2)^2}\\\\d = \sqrt{36 + 4}\\\\d = \sqrt{40}\\\\d \approx 6.325\\\\[/tex]

Segment AB is roughly 6.325 units long. You could use the pythagorean theorem as an alternative route instead of the distance formula.

If you repeated this process for the other segment lengths, then you should get these other approximate lengths.

BC = 6.083CD = 6.325

Add up those three results:

AB+BC+CD = 6.325+6.083+6.325 = 18.733

The entire cable is roughly 18.733 units long.

Since 1 unit = 10 feet, we'll multiply that result by 10.

18.733*10 = 187.33 feet

This rounds to 187 feet which is the approximate length of the cable.

The length of the cable will be 187.2 feet long.

What is the distance between two points?

Let one point be (x, y) and another point be (h, k). Then the distance between the points will be

D² = (x - h)² + (y - k)²

From the diagram, the length between (0, 3) and (6, 5), (6, 5) and (12, 4), and (12, 4) and (18, 2) will be the length of the cable (L).

[tex]\rm L = \sqrt{(6 - 0)^2 + (5-3)^2} + \sqrt{(12 - 6)^2 + (4 - 5)^2} + \sqrt{(18 - 12)^2 + (2 - 4)^2}\\[/tex]

Simplify the equation, then we have

L = √40 + √37 + √40

L = 6.32 + 6.08 + 6.32

L = 18.72 units

L = 18.72 x 10

L = 187.2 ft

The length of the cable will be 187.2 feet long.

Learn more about the distance between two points here:

https://brainly.com/question/18296211

#SPJ2

Help! I’ll give you the brainly answer if you help!

Answers

Answer:

2,78,31,64,4-2,10-6,54,-97,-38,-8-7,-4-5,-11-1,-16

Please help by September 7th.

Answers

Answer:

The first of the 3 numbers is 11.

Step-by-step explanation:

Well all three would be 11,12,13 because 11+12+13=36. First number is 11

Help fast! If you answer right ill give best khan academy

Answers

Answer:

17 I think it's 17 considering the 45 went to 35

Can you please help me solve this problem! And can you add step by step, please! Not really sure what to do?

Answers

Answer:

quadrilateral has 4 sides

so 104°+40°+110°+x=360°

254°+x=360°

collect like terms

x=360-254

x= 106

;- x=106

which is (c)

Answer:

x = 106°

Step-by-step explanation:

Using the angle marked 110° as my starting point,

One can use angles on a straight line sum up to 180° to find the angle that adds up to 110° which makes it 180,

thus 70°.

moving on,

tackling with the angle marked 40°, Using the fact that angles on a straight line sum up to 180°, the angle obtained will be 140° (40° + a = 180, a = 180° -40°, a = 140°)

Using the angle marked 104°, Just like the previous one Using the principle that angles on a straight line sums up to 180°, then the unknown angle will be 76°.

Finding all the other interior angles angles in the quadrilateral except the angle in line with the x,

the next step to take is to add up all the angles Using any variable and equate it to 360°

why? angles in this type of quadrilateral equals 360,

That is,

140° + 76° + 70° + y = 360

286 + y= 360

y = 360 - 286

y = 74

The final step now is to use the principle, ( angles on a straight line sums up to 180)

74° + x = 180

x = 180 - 74

x = 106°

3k = 126 ??????????????????????????

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\boxed{\mathsf{3k = 126}}[/tex]

[tex]\huge\boxed{\textsf{\bf DIVIDE 3 to BOTH SIDES}}[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{3k}{3}= \dfrac{126}{3}}}}[/tex]

[tex]\huge\boxed{\mathsf{\bf CANCEL\ out: \dfrac{3}{3}\ because\ it\ gives \ you\ 1}}}[/tex][tex]\huge\boxed{\bf KEEP: \dfrac{}{}\ because\ it\ answers\ for\ the\ }\\\huge\boxed{\bf k-value}[/tex]

[tex]\huge\boxed{\mathsf{k = \dfrac{126}{3}}}\\\huge\boxed{\mathsf{\dfrac{126}{3} = k}}[/tex]

[tex]\huge\boxed{\textsf{\bf SIMPLIFY ABOVE}}[/tex]

[tex]\huge\boxed{\mathsf{Therefore, your \ answer \ is: k = 42}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

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