1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ololo11 [35]
3 years ago
9

A tourist starts to walk up a mountain path that is 31 miles long at the rate of 4 miles per hour. After walking for a while, he

gets tired and decides to get a taxi. The taxi gets him to the top traveling at a constant speed of 50 mph. If the tourist reaches the destination 2 hours after he started, what distance does he have to pay the cab driver for?
Mathematics
1 answer:
Sunny_sXe [5.5K]3 years ago
5 0

Answer:

He pays to the cab driver for 25 miles.

Step-by-step explanation:

Consider the provided information.

Let us consider he walks x miles at the rate of 4 miles per hour.

As we know Time=\frac{Distance}{Speed}

Therefore, time taken is: Time=\frac{x}{4}

He get a taxi for (31-x) miles at the rate of 50 miles per hour.

Therefore, time taken is: Time=\frac{31-x}{50}

It took 2 hours after he started.

That means the sum of time take is 2 hours.

\frac{x}{4}+\frac{31-x}{50}=2

\frac{25x+62-2x}{100}= 2

23x+62= 200

23x= 138

x= 6

Hence he walk 6 miles and he get a taxi for 31-6=25 miles.

He pays to the cab driver for 25 miles.

You might be interested in
The first number of three consecutive even integers equals the sum of the second and third. Find the three numbers.
Arlecino [84]

The first integer (x) is equal to the consecutive even integers, x+2, x+4.

x = (x+2) + (x+4)

x = 2x + 6

x - 6 = 2x

x = -6 (First integer)


+2

-4 (Second integer)


+4

-2 (Third integer)


Integers: -6, -4, -2

Equation: x = (x+2) + (x+4)

8 0
3 years ago
Read 2 more answers
A spinner is split into 4 equal parts labeled 1, 2, 3, and 4.
LiRa [457]

Answer:50%

Step-by-step explanation:

4 0
3 years ago
A quadrilateral has vertices at $(0,1)$, $(3,4)$, $(4,3)$ and $(3,0)$. Its perimeter can be expressed in the form $a\sqrt2+b\sqr
seraphim [82]

Answer:

a + b = 12

Step-by-step explanation:

Given

Quadrilateral;

Vertices of (0,1), (3,4) (4,3) and (3,0)

Perimeter = a\sqrt{2} + b\sqrt{10}

Required

a + b

Let the vertices be represented with A,B,C,D such as

A = (0,1); B = (3,4); C = (4,3) and D = (3,0)

To calculate the actual perimeter, we need to first calculate the distance between the points;

Such that:

AB represents distance between point A and B

BC represents distance between point B and C

CD represents distance between point C and D

DA represents distance between point D and A

Calculating AB

Here, we consider A = (0,1); B = (3,4);

Distance is calculated as;

Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

(x_1,y_1) = A(0,1)

(x_2,y_2) = B(3,4)

Substitute these values in the formula above

Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

AB = \sqrt{(0 - 3)^2 + (1 - 4)^2}

AB = \sqrt{( - 3)^2 + (-3)^2}

AB = \sqrt{9+ 9}

AB = \sqrt{18}

AB = \sqrt{9*2}

AB = \sqrt{9}*\sqrt{2}

AB = 3\sqrt{2}

Calculating BC

Here, we consider B = (3,4); C = (4,3)

Here,

(x_1,y_1) = B (3,4)

(x_2,y_2) = C(4,3)

Substitute these values in the formula above

Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

BC = \sqrt{(3 - 4)^2 + (4 - 3)^2}

BC = \sqrt{(-1)^2 + (1)^2}

BC = \sqrt{1 + 1}

BC = \sqrt{2}

Calculating CD

Here, we consider C = (4,3); D = (3,0)

Here,

(x_1,y_1) = C(4,3)

(x_2,y_2) = D (3,0)

Substitute these values in the formula above

Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

CD = \sqrt{(4 - 3)^2 + (3 - 0)^2}

CD = \sqrt{(1)^2 + (3)^2}

CD = \sqrt{1 + 9}

CD = \sqrt{10}

Lastly;

Calculating DA

Here, we consider C = (4,3); D = (3,0)

Here,

(x_1,y_1) = D (3,0)

(x_2,y_2) = A (0,1)

Substitute these values in the formula above

Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

DA = \sqrt{(3 - 0)^2 + (0 - 1)^2}

DA = \sqrt{(3)^2 + (- 1)^2}

DA = \sqrt{9 +  1}

DA = \sqrt{10}

The addition of the values of distances AB, BC, CD and DA gives the perimeter of the quadrilateral

Perimeter = 3\sqrt{2} + \sqrt{2} + \sqrt{10} + \sqrt{10}

Perimeter = 4\sqrt{2} + 2\sqrt{10}

Recall that

Perimeter = a\sqrt{2} + b\sqrt{10}

This implies that

a\sqrt{2} + b\sqrt{10} = 4\sqrt{2} + 2\sqrt{10}

By comparison

a\sqrt{2} = 4\sqrt{2}

Divide both sides by \sqrt{2}

a = 4

By comparison

b\sqrt{10} = 2\sqrt{10}

Divide both sides by \sqrt{10}

b = 2

Hence,

a + b = 2 + 10

a + b = 12

3 0
2 years ago
Write a subtraction that will give the same difference as 15-7
Georgia [21]
15 - 7 = 8 so there are many you can do like:
16 - 8 = 8
20 - 12 = 8
22 - 14 = 8
and so on, there are many.




8 0
3 years ago
The volume of a rectangular tank is 20 000 cm3 . Given that the length is 40 cm and width is 25 cm, find its height
olga nikolaevna [1]

<em>answer \\ 20 \: cm \\ solution \\ volume = 20000 \:  {cm}^{3}  \\ length = 40 \: cm \\ breadth = 25 \: cm \\ height =  \\ now \\ v = l \times b \times h \\  \:  \:  \:  \:  \:  \: or \: 20000 = 40 \times 25 \times h \\ or \: 20000 = 1000 \times h \\ or \: h =  \frac{20000}{1000}  \\ h = 20 \: cm \\ hope \: it \: helps</em>

5 0
2 years ago
Read 2 more answers
Other questions:
  • Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 2.4 h, and Car B traveled the dis
    10·1 answer
  • 1) Describe the difference between simple and compound interest.
    14·1 answer
  • Help Me out with this question plz thx​
    9·2 answers
  • Make r the subject of the formula t=<img src="https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7Br-3%7D" id="TexFormula1" title="\frac{r}{
    10·1 answer
  • Wanda has eaten 25 of the 28 grapes in her bowl, so she is 25/28 of the way to finishing her snack. Which statement best describ
    15·1 answer
  • Mass = 100g, Volume = 20ml, what is density?​
    13·2 answers
  • Find the slope of the line with points (-1,-2) (2,7)
    9·1 answer
  • PLEASE HELP ASAP I FORGOT ABOUT THIS QUESTION AND THIS IT IS THE LAST QUESTION- LOL
    6·1 answer
  • ILL GIVE A BRAINLIEST FOR THE ANSWER THAT HELPS ME THE MOSTT.​
    6·1 answer
  • HELP!!<br> what is 23x+(4-5b)
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!