Mathematics, 12.08.2020 06:01 JakerGamer

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?

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Answer from: mmaglaya1

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

Answer from: Quest

entering that problem on the tube might get you an answer

Answer from: Quest

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

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