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
The sum of a number and 9 is multiplied by -2 and the answer is -8
nadya68 [22]
9(-2)+x=-8
And x would be positive 26
7 0
3 years ago
In 20 years, Finn will be 3 times as old as he is right now. How old is he right now?​
Bumek [7]
I think it is 60 years old?
3 0
1 year ago
The school will not announce a snow day unless there is 10 inches of snow on the ground. If it had already snowed 1.5 inches how
Dennis_Churaev [7]
21 more inches. Hey, you're welcome.
7 0
3 years ago
Determine the value of x.<br><br>A. 4√2<br><br>B. 2/√2<br><br>C. 2√2<br><br>D. 2
ZanzabumX [31]

Answer:

\huge\boxed{\sf C.}

Step-by-step explanation:

sin 45 = opposite / hypotenuse

<u>Where opposite = x , hypotenuse = 4</u>

sin 45 = x / 4

\sf \frac{\sqrt{2} }{2 } = \frac{x}{4} \\\\x = \frac{4\sqrt{2} }{2} \\\\x = 2\sqrt{2} \\\\\rule[225]{225}{2}

Hope this helped!

<h3>~AH1807</h3>
3 0
3 years ago
Determine the values of x on which the function f(x)=2x^2-x-15/4x^2-12x is discontinuous and verify the type of discontinuity at
melomori [17]
<span>Determine the values of x on which the function f(x)=2x^2-x-15/4x^2-12x is discontinuous and verify the type of discontinuity at each point.

A.There is a vertical asymptote at 0 and a hole at 3.
B.There are vertical asymptotes at -5/2 & 0 and a hole at 3.
C.There is a vertical asymptote at 3 and a hole at 0.
D.There are vertical asymptotes at 0 & 3.
</span>
Result:
(-7/4)x^2-13x

The roots are:
x= -52/7
x=0

See attached pictures.

6 0
3 years ago
Read 2 more answers
Other questions:
  • A right triangle has legs that are 10.1 inches and 12.2 inches long. what is the approximate length of the hypotenuse?
    12·2 answers
  • X<br> 17- 5 +<br> 17<br> 싸<br> What is X? ?
    14·1 answer
  • Segment AB has endpoints at −2 and 12. What is the coordinate of its midpoint?
    7·1 answer
  • 2. Write the probability of each event when choosing one card at random from a standard
    14·1 answer
  • What is 4and2/14 as an improper fraction in lowest terms
    5·2 answers
  • Also this pls pls pls
    12·1 answer
  • Plz answer the questions
    8·1 answer
  • Slope of -2<br> passing through <br> the point (-11,16)
    15·1 answer
  • Plzz help for brianly
    7·2 answers
  • You cut grass with a friend for 5 hours and each got paid 8 dollars an hour. On your way home you stopped by a convenient store
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!