A man walks for x hours at a speed of
(x + 1) km/h and cycles for (x - 1) hours at
a speed of (2x + 5) km/h. If the total distance
travelled is 90 km, x

Answers

Answer 1

Given:

A man walks for x hours at a speed of  (x + 1) km/h and cycles for (x - 1) hours at  a speed of (2x + 5) km/h.

Total distance  travelled is 90 km.

To find:

The value of x.

Solution:

We know that,

[tex]Speed=\dfrac{Distance}{Time}[/tex]

[tex]Speed\times Time=Distance[/tex]

A man walks for x hours at a speed of  (x + 1) km/h, so walking distance is

[tex]D_1=(x+1)(x)[/tex] km

The man cycles for (x - 1) hours at  a speed of (2x + 5) km/h, so the cycling distance is

[tex]D_2=(2x+5)(x-1)[/tex] km

Now,

Total distance = 90 km

[tex]D_1+D_2=90[/tex]

[tex](x+1)x+(2x+5)(x-1)=90[/tex]

[tex]x^2+x+2x^2-2x+5x-5-90=0[/tex]

[tex]3x^2+4x-95=0[/tex]

[tex]3x^2+19x-15x-95=0[/tex]

[tex]x(3x+19)-5(3x+19)=0[/tex]

[tex](3x+19)(x-5)=0[/tex]

[tex]3x+19=0\text{ and }x-5=0[/tex]

[tex]x=\dfrac{-19}{3}\text{ and }x=5[/tex]

Time cannot be negative. So, the only possible value of x is 5.


Related Questions

You buy three hamburgers and a soda for $14.20. If sodas cost $2.95, what is the price of each hamburger?​

Answers

Answer:

3.75

Step-by-step explanation:

14.20-2.95=11.25÷3=3.75 per burger

what is two and a half added to four and a half?

Answers

Answer:

7

Step-by-step explanation:

What is the area of the circle ?

Answers

Answer:

113.04 [tex]m^{2}[/tex]

Step-by-step explanation:

Area of a circle is π x [tex]r^{2}[/tex].

I'm assuming that you're using 3.14 as π.

Since the radius of the circle is 6 m, all you need to do is plug it in!

Area = 3.14 × [tex](6)^{2}[/tex]

Area = 3.14 × 36

Area = 113.04 [tex]m^{2}[/tex], which is the third answer choice.

I think it is 113.04

HELP PLZ DUE IN 30 MIN


A. none


B. b // c


C. a // c


D. a // b

Answers

9514 1404 393

Answer:

  D.  a ║ b

Step-by-step explanation:

If we figure the other angle of each linear pair, we can directly compare angles to see if corresponding angles are the same. Where they are the same, the lines are parallel.

  Line a is parallel to line b.

Sarah is playing a video game that allows her to double her coins each hour. The game starts with 4 coins and Sarah plays the game for 2 hours. How many coins will she have at the end of the two hours.

Answers

Answer:

16 coins

Step-by-step explanation:

At first: 4 coins

First hour: 4 x 2 = 8

Second hour: 8 x 2 = 16

Total coins: 16 coins

nine hundred nine thousandths in numeric form

Answers

Answer:

900,000

I think is the answer

PLEASE I NEEED HELP ANYONE

Answers

Answer: 264 cubic centimeters

8*8*1=64

8*5*5=200

200+64=264

Doug has two German Shepherds. The
larger dog weighs 70 1/2 pounds. If the
smaller dog weighs 75% as much as the
larger dog, find the smaller dog's weight.
wait ugh i asked the wrong question help pls and thank you

Answers

Answer:

52 7/8 pounds

Step-by-step explanation:

Find the smaller dog's weight by multiplying the larger dog's weight by 0.75:

70.5(0.75)

= 52.875 or 52 7/8 pounds

So, the smaller dog weighs 52 7/8 pounds

The required weight of the smaller dog is 52.875 pounds.

Given that,
Doug has two German Shepherds. The larger dog weighs 70 1/2 pounds. If the smaller dog weighs 75% as much as the larger dog, To find the smaller dog's weight.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements.

What is percentages?

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Let the weight of the smaller dog be x,
The weight of the smaller dog is 75% of the larger dog
x = 75% of 70 1/2
x = 0.75 * 70.5
x = 52.875

Thus, the required weight of the smaller dog is 52.875 pounds.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ2

CHARITY This year, James raised $95 for an animal shelter. This is 5
times the amount he saved. The equation 5x = 95 can be used to find last
year's fundraising amount. Find last year's fundraising amount.

Please help I have know clue what to do!!

Answers

Answer: Hi, sorry if I’m late to answering but the answer is 19

Step-by-step explanation:

You divide each number in the equation by 5. So, 5x divided by 5 = 1. We cannot use 5 divided by 5 because it will equal 1 so we ignore that and go to 95 divided by 5 = 19. Therefore, 19 is your answer!!! (Hope this helped)

Jenny has 45 tennis balls.
Sal had 20 tennis balls, but he gave 6 of them to Joe.
How many tennis balls do Jenny and Sal have now?

Answers

Answer:

45 and 14 are the correct answer

Jenny has 45 and Sal has 14

3x + 4y = 12
2x-2y = 10

Answers

3x+4y=12
4x-4y=20
7x=32
x=32/7
2y=64/7 - 10

Use the figure to find the measures of the numbered angles.


∠1 = ∘

∠2 = ∘

∠3 = ∘

∠4 = ∘

∠5 = ∘

∠6 = ∘

Answers

Physiological (1 point)
The processes and functions of the body
The processes of the mind
Social needs, social behaviors, and social problems
Otraits that increase the possibility of developing an illness or disease

can someone please help me and show work ?

Answers

Answer:

(1). x = 14 ; (2). 70°

Step-by-step explanation:

(1). m∠ACD = m∠A + m∠B

6x + 2 = (2x + 1) + (3x + 15)

6x - 5x = 14

x = 14

(2). m∠ABC = 180° - m∠CBD = 140°

m∠A = m∠C = 140° ÷ 2 = 70°

I DONT GET IT ill give u pointsss answerr

Answers

I think you multiply 5.65 by 10 -7 meters and you’ll get your answer. Or 1e+9

What is the reasoning for this statement?

Answers

Answer:

there is a black photo

Step-by-step explanation:

make sure to check properly

Select the correct answer.
Which equation represents a circle?

Answers

Answer:

C

Step-by-step explanation: each side by 4 and you get the radius as 2 and the center at 0,0.

Answer: C

Step-by-step explanation: I got this right on Edmentum.

If I have an equation in which x = pounds, and y = total cost, can I substitute quarts into the equation yes or no ?

Answers

Answer:

Yes you can, you just need to make x be times by 4.

Step-by-step explanation:

4 quarts in a gallon

If the area A of a triangle is 72, and the height h is equal to the length of the base b, what is the length of the base?

A= 1/2 bh

Select one
A. 9
B. 12
C. 11
D. 5

Answers

Answer:

option B

Step-by-step explanation:

let the height=x

base=x

Area=½bh

72=½x•x

72×2=x²

144=x²

x=√144=12

Answer:

12

Step-by-step explanation:

12 x 12= 144

144/2= 72

A right triangle is formed by joining three
squares at their vertices.

Which equation can be used to find the length
of x?

Answers

Answer:

D. x² = 576 + 7²

Step-by-step explanation:

i got this correct on my homework :)

simplify the following
a.) 2^7 x 2

Answers

Answer:

256

Step-by-step explanation:

i think it is 256.i hope it was that

Answer:

Step-by-step explanation:

Here you go mate;

STEP 1

2^7 x 2  equation

STEP 2

2^7 x 2  simplify

(2^7)(x^2)

STEP 3

128^2  multiply

answer

16384

Factorise:
(a).125m^3+27n^3+225m^2n+135mn^2

(B). 64a^3-144a^2b+108ab^2-27b^3

Plz answer, it's urgent. ​

Answers

Answer:

a)(5m+3n)^3 b)(4a-3b)^3

Step-by-step explanation:

a)125m^3+27n^3+225m^2 n+135mn^2

Use the binomial cube formula, a^3+3a^2

b+3ab^2+b^3=(a+b)^3, where a=5m and b=3n.

(5m+3n)^3

b)64a^3-144a^2 b+108ab^2-27b^3

Use the binomial cube formula, p^3-3p^2q+3pq^2-q^3=(p-q)^3, where p=4a and q=3b.

(4a-3b)^3

Please answer correctly !!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!

Answers

Answer:

x = 8

Step-by-step explanation:

well using the theorem we have

[tex]\frac{6}{9}=\frac{x}{12}\\\\\frac{2}{3}=\frac{x}{12}\\\\12[\frac{2}{3}]=12[\frac{x}{12}]\\\\4\cdot 2=x\\\\x=8[/tex]

Marta has twice as much money as Heidi. Together they have $36. Write a system of equations that could be used to determine much money each person has​

Answers

x + 2x = 36

3x = 36
/3
x = 12

Martha has $24 and Heidi has $12

What is the value for x=

Answers

Here you go. This is the answer to your question.

Answer:

x = 2[tex]\sqrt{5}[/tex]

Step-by-step explanation:

Since the 2 legs are congruent, both 6 then the triangle is isosceles.

The line from the vertex to the base is a perpendicular bisector, dividing the base into 2 parts of 4 units.

Using Pythagoras' identity in one of the right triangles.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 4² = 6²

x² + 16 = 36 ( subtract 16 from both sides )

x² = 20 ( take the square root of both sides )

x = [tex]\sqrt{20}[/tex] = [tex]\sqrt{4(5)}[/tex] = 2[tex]\sqrt{5}[/tex]

How many solutions does the following linear equations have: 7(2+5x)=3x+14

Answers

Um I think only one, pretty sure

Write an equation that represents the line.
Use exact numbers.

Answers

Answer:

y=3/4x+(-4.5)

Step-by-step explanation:

Kelsea and Landon are playing in a park standing 100 feet away from each other. They both see a bird flying above them. The angles of elevation from each person to the bird are shown. How high is the bird from the ground? Round your answer to the nearest tenth. The angle for landon is 45 degrees the angle for kelsea is 20

Answers

Answer:

26.68 ft

Step-by-step explanation:

Let a represent the distance from Kelsea to the bird and b be the distance from Landon to the bird.

Let x = angle of the bird. Hence:

x + 45 + 20 = 180 (sum of angles in a triangle)

x + 65 = 180

x = 180 - 65

x = 115°

Using sine rule:

[tex]\frac{100\ ft}{sin(115)} =\frac{a}{sin(45)} =\frac{b}{sin(20)} \\\\\frac{100\ ft}{sin(115)} =\frac{a}{sin(45)}\\\\a=\frac{100\ ft}{sin(115)} *sin(45)\\\\a=78\ ft\\[/tex]

Let h = height of the bird to the ground. Since a right angle is formed. hence:

[tex]\frac{h}{sin(20)} =\frac{78}{sin(90)} \\\\h=\frac{78}{sin(90)}*sin(20)\\\\h=26.68\ ft[/tex]

Find the area of the shape. Need an answer immediately.

Answers

Answer:

A= 113.1 (I rounded my answer)

Step-by-step explanation:

A=πr^2=π·6^2=113.09734

Quick I need helppp!!

4.7= a + 3.09; a= 0.8, 0.98, 1.61, 7.79

Answers

Answer:

1.61

Step-by-step explanation:

Just subtract 4.7 by 3.09

Need HELP ASSAP -8/5 times -5/1

Answers

Answer:8

Step-by-step explanation: negative times negative =positive

and times 8/5 by 5/1  .

When multiplying fractions, simply multiply the numerators together and multiply the denominators together.

-8 * -5 = 40

5 * 1 = 5

-8/5 * -5/1 = 40/5

40/5 = 8

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