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
finlep [7]
3 years ago
8

A cyclist travels at $20$ kilometers per hour when cycling uphill, $24$ kilometers per hour when cycling on flat ground, and $30

$ kilometers per hour when cycling downhill. On a sunny day, they cycle the hilly road from Aopslandia to Beast Island before turning around and cycling back to Aopslandia. What was their average speed during the entire round trip?
Mathematics
1 answer:
aleksley [76]3 years ago
6 0

Answer:

Average speed during the trip = 24 km/h

Step-by-step explanation:

Given:

Speed of cyclist uphill, v_1 = 20 km/hr

Speed of cyclist on flat ground = 24 km/h

Speed of cyclist downhill, v_2 = 30 km/h

Cyclist has traveled on the hilly road to Beast Island from Aopslandia and then back to Aopslandia.

That means, one side the cyclist went uphill will the speed of 20 km/h and then came downhill with the speed of 30 km/h

To find:

Average speed during the entire trip = ?

Solution:

Let the distance between Beast Island and Aopslandia = D km

Let the time taken to reach Beast Island from Aopslandia = T_1\ hours

Formula for speed is given as:

Speed = \dfrac{Distance}{Time}

v_1 = 20 = \dfrac{D}{T_1}

\Rightarrow T_1 = \dfrac{D}{20} ..... (1)

Let the time taken to reach Aopslandia back from Beast Island = T_2\ hours

Formula for speed is given as:

Speed = \dfrac{Distance}{Time}

v_2 = 30 = \dfrac{D}{T_2}

\Rightarrow T_2 = \dfrac{D}{30} ..... (2)

Formula for average speed is given as:

\text{Average Speed} = \dfrac{\text{Total Distance}}{\text{Total Time Taken}}

Here total distance = D + D = 2D km

Total Time is T_1+T_2 hours.

Putting the values in the formula and using equations (1) and (2):

\text{Average Speed} = \dfrac{2D}{T_1+T_2}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{D}{20}+\dfrac{D}{30}}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{30D+20D}{20\times 30}}\\\Rightarrow \text{Average Speed} = \dfrac{2D\times 20 \times 30}{{30D+20D}}\\\Rightarrow \text{Average Speed} = \dfrac{1200}{{50}}\\\Rightarrow \bold{\text{Average Speed} = 24\ km/hr}

So, Average speed during the trip = 24 km/h

You might be interested in
A painting shaped like a circle has a diameter of 20 inches. A circular frame extends 2 inches around the edge of the painting.
Natasha_Volkova [10]
So hmm check the picture below

8 0
3 years ago
Find the intersection points using substitution or elimination for each system of equations:
natka813 [3]

Answer:

Step-by-step explanation:

Okay, so I think I know what the equations are, but I might have misinterpreted them because of the syntax- I think when you ask a question you can use the symbols tool to input it in a more clear way, otherwise you can use parentheses and such.

Problem 1:

(x²)/4 +y²= 1

y= x+1

*substitute for y*

Now we have a one-variable equation we can solve-

x²/4 + (x+1)² = 1

x²/4 + (x+1)(x+1)= 1

x²/4 + x²+2x+1= 1

*subtract 1 from both sides to set equal to 0*

x²/4 +x^2+2x=0

x²/4 can also be 1/4 * x²

1/4 * x² +1*x² +2x = 0

*combine like terms*

5/4 * x^2+2x+ 0 =0

now, you can use the quadratic equation to solve for x

a= 5/4

b= 2

c=0

the syntax on this will be rough, but I'll do my best...

x= (-b ± √(b²-4ac))/(2a)

x= (-2 ±√(2²-4*(5/4)*(0))/(2*(5/4))

x= (-2 ±√(4-0))/(2.5)

x= (-2±2)/2.5

x will have 2 answers because of ±

x= 0 or x= 1.6

now plug that back into one of the equations and solve.

y= 0+1 = 1

y= 1.6+1= 2.6

Hopefully this explanation was enough to help you solve problem 2.

Problem 2:

x² + y² -16y +39= 0

y²- x² -9= 0

6 0
3 years ago
Which is greater 1/4 or 0.4
Likurg_2 [28]

Answer:

0.4

Step-by-step explanation:

1/4 = 0.25

3 0
3 years ago
Read 2 more answers
The sum of 9and -16 increased by 4
LenaWriter [7]

Answer:

-3

Step-by-step explanation:

The statement is,

→ Sum of 9 and -16 increased by 4

The equation will be,

→ {9 +(-16)} + 4

→ (9 - 16) + 4

→ -7 + 4

→ [ -3 ]

Hence, the solution is -3.

7 0
2 years ago
What is the equation of a circle with center (-3, -1) that contains the point (1, 2)?
Leno4ka [110]
So, we know the center is at -3,-1, ok

hmmm what's the radius anyway?   well, we know that there's a point at 1,2 that is on the circle's path...hmmmm what's the distance from the center to that point?  well, is the radius, let's check then.

\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ -3}}\quad ,&{{ -1}})\quad 
%  (c,d)
&({{ 1}}\quad ,&{{ 2}})
\end{array}\qquad 
%  distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
r=\sqrt{[1-(-3)]^2+[2-(-1)]^2}\implies r=\sqrt{(1+3)^2+(2+1)^2}
\\\\\\
r=\sqrt{16+9}\implies r=\sqrt{25}\implies r=5

so, what's the equation of a circle with center at -3, -1 and a radius of 5?

\bf \textit{equation of a circle}\\\\ 
(x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
\qquad 
\begin{array}{lllll}
center\ (&{{ h}},&{{\quad  k}})\qquad 
radius=&{{ r}}\\
&-3&-1&5
\end{array} 
\\\\\\\
[x-(-3)]^2+[y-(-1)]^2=5^2\implies (x+3)^2+(y+1)^2=25
7 0
3 years ago
Other questions:
  • A library contains 2000 books. there are 3 times as many non-fiction books as fiction books. write and solve a system of equatio
    11·1 answer
  • A piece of cloth is folded into a square with a side length measuring x inches. When it is unfolded, it has an area of x2 + 27x
    7·2 answers
  • If Bart has 20$ and Andy took $19.65 how much does Bart have
    5·1 answer
  • a team of 4 people participate in a 400-yard relay race each team member runs the same distance the team completes the race in 5
    12·1 answer
  • 7.50x +4.50y = 2,212.5<br> x+y = 375
    12·1 answer
  • Simplify answer, round to nearest 10th in radical form
    10·1 answer
  • What is the value of x in the equation 24−2x=16?<br> a 4<br> b 8<br> c 12<br> d 20
    13·1 answer
  • Consider the inequality -5(x+7) &lt;-10. write an inequalityrepresenting the soulution for x.
    6·1 answer
  • The question is in the picture ​
    14·2 answers
  • 3(x+4) Please answer :(
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!