TakahiroMaeda

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UsernameTakahiroMaeda
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Questions 8
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 #1
avatar+676 
+3

Okay Lets do this:

 

Distance flown by the Airplane = 3500 Kilometers

Distance traveled by the train = 600 Kilometers

Lets make x the taken by the Airplane

Because of this, it would make sense that the time taken to travel 600 Kilometers is also x.

Now to find out the speed of the Airplane, the forumla is 

$${\frac{{\mathtt{3\,500}}}{{\mathtt{x}}}}$$

Now to find out the speed of the Train, the forumla is

$${\frac{{\mathtt{600}}}{{\mathtt{x}}}}$$

Now let us use what we already know.

$${\frac{{\mathtt{3\,500}}}{{\mathtt{X}}}} = {\mathtt{5}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{600}}}{{\mathtt{X}}}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{50}}$$

$${\frac{{\mathtt{3\,500}}}{{\mathtt{x}}}} = \left({\frac{{\mathtt{3\,000}}}{{\mathtt{x}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{50}}\right)$$

Now we need to eradicate the x

So we multiply x to both sides.

$${\mathtt{3\,500}} = {\mathtt{3\,000}}{\mathtt{\,\small\textbf+\,}}{\mathtt{50}}{\mathtt{\,\times\,}}{\mathtt{X}}$$

Now we need to use some basic algebra knowledge to solve this. Let us move x to one side and the numbers on the other. We will get

$${\mathtt{x}} = {\mathtt{10}}$$

Now, lets go back to what we know already know and substitute.

For the Plane:

$${\mathtt{SPEED}} = {\frac{{\mathtt{3\,500}}}{{\mathtt{X}}}}$$

$${\mathtt{SPEED}} = {\frac{{\mathtt{3\,500}}}{{\mathtt{10}}}}$$

$${\mathtt{SPEED}} = {\mathtt{350}}{KM}$$per hour

For the Train:

$${\mathtt{SPEED}} = {\frac{{\mathtt{600}}}{{\mathtt{X}}}}$$

$${\mathtt{SPEED}} = {\frac{{\mathtt{600}}}{{\mathtt{10}}}}$$

$${\mathtt{SPEED}} = {\mathtt{60}}{KM}$$ per hour.

There we go.

The Speed of the plane was 350KM per hour 

and the speed of the train was 60 Km per hour

May 23, 2014
 #2
avatar+676 
0

 all-them-marvel-feels is correct!

Your equation is written as an Expression therefore making no sense. I would reword the equation for clarity. But, given that 3x=21 is what you mean. You have been answered.

May 23, 2014
 #1
avatar+676 
+13

Right then!

Lets solve this together!

First of all, we will need to turn all of the Mixed Fractions into improper fraction for ease of understanding.

To turn an Mixed Number or Mixed Fraction into an improper fraction the steps are quite simple. First look at the denominator. Lets use an Mixed Number in the equation.

2 1/3.

The denominator is 3 correct? Now we need to look at the Whole number. That is 2. Now we just multiply then together.

$${\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{3}}$$

What does that equal? 6.

Now we just add the 6 to the numerator. So we get a fraction of:

$${\frac{{\mathtt{7}}}{{\mathtt{3}}}}$$

Now we do that for all the mixed numbers.

So we should end up with:

$${\frac{{\mathtt{7}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{8}}}{{\mathtt{5}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{19}}}{{\mathtt{6}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{11}}}{{\mathtt{4}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{22}}}{{\mathtt{5}}}}$$

Now we reach the hardest part of solving this equation.

What is the LCM of all of these numbers?

LCM is Lowest Common Multiple.

So what is the lowest number that all 5 of these numbers go into. 

Let me guide you through this step.

Lets start with any number.

20?

Okay. Does 3 Go into 20?

Sadly no. So this does not qualify as the Lowest Common Multiple.

60?

Does 3 Go into 60? Yes!

Does 5 Go into 60? Yes!

Does 4 Go into 60? Yes!

Does 6 Go into 60? Yes!

We skip the other one, because there are two 5's, making writing it again useless.

How then we found a number, we will need to calculate the amount of the number goes to the other number.

So.. How many 3's go into 60?

20.

5 to 60?

12.

4 to 60?

15.

6 to 60?

10. 

Now lets utilise this!

Back to the Equation.

$${\frac{{\mathtt{7}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{8}}}{{\mathtt{5}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{19}}}{{\mathtt{6}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{11}}}{{\mathtt{4}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{22}}}{{\mathtt{5}}}}$$

We want to the the demoninator the LCM. Or in this equation 60.

Go do that, we must multiply what we do to the demoninator also to the Numerator.

So. For Example:

$${\frac{{\mathtt{7}}}{{\mathtt{3}}}}$$

What do we need to do with the Demoninator to get it to 60?

Multiply by 20!

So we multiply both the top and the bottom with 20.

$${\frac{\left({\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{20}}\right)}{\left({\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{20}}\right)}}$$

We get:

$${\frac{{\mathtt{140}}}{{\mathtt{60}}}}$$

Now do the same to all the other fractions so we will get:

$${\frac{{\mathtt{140}}}{{\mathtt{60}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{96}}}{{\mathtt{60}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{190}}}{{\mathtt{60}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{165}}}{{\mathtt{60}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{264}}}{{\mathtt{60}}}}$$

Now add them all together.

$${\frac{{\mathtt{140}}}{{\mathtt{60}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{96}}}{{\mathtt{60}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{190}}}{{\mathtt{60}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{165}}}{{\mathtt{60}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{264}}}{{\mathtt{60}}}} = {\frac{{\mathtt{57}}}{{\mathtt{4}}}} = {\mathtt{14.25}}$$

There we are! The Answer.

14.25

May 23, 2014