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John walks at 4km/h and runs at 12 km/h . He completes a journey in two parts. If he walks the first part and runs the second part it takes him 3 hours. If he runs the first part and walks the second part it takes him 2 hours. Find the lengths of the two parts of the journey .

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facundo3141592

Answer: The first part is 10.5 miles long and the second part is 4.5 miles long.

Step-by-step explanation:

We have the relationship

Velocity = distance/time.

or:

Time = distance/velocity.

If the first part of the journey is A, and the second part is B, we have a system of equations:

A/4 + B/12 = 3

A/12 + B/4 = 2

Now we need to solve this, the first step is isolating one of the variables in one of the equations, let's isolate A in the first equation:

A/4 + B/12 = 3

A + 4*B/12 = A + B/3 = 4*3 = 12

A = 12 - B/3

now we can replace it in the other equation and get:

A/12 + B/4 = 2

(12 - B/3)/12 + B/4 = 2

1 - B/36 + B/4 = 2

B(1/4 - 1/36) = 2- 1 = 1

B*(9/36 - 1/36) = 1

B = 1*36/8 = 4.5

A = 12 - B/3 = 12 - 4.5/3 = 10.5

Then the first part is 10.5 miles long and the second part is 4.5 miles long.

olayemiolakunle65

Answer:

The length of the first path is 10.5Km, and the length is the second path is 4.5Km.

Step-by-step explanation:

The speed of an object is the rate of the distance covered to the time taken.

i.e speed = [tex]\frac{distance}{time}[/tex]

⇒ time = [tex]\frac{distance}{speed}[/tex]

Let the length of first path be represented by [tex]l_{1}[/tex], and that of the second path by [tex]l_{2}[/tex].

In the first case, he walks first path and runs the second path.

So that:

[tex]\frac{l_{1} }{4}[/tex] + [tex]\frac{l_{2} }{12}[/tex] = 3   ............... (1)

In the second case, he runs the first path and walks the second path.

So that:

[tex]\frac{l_{1} }{12}[/tex] + [tex]\frac{_{2} }{4}[/tex] = 2     ................. (2)

From equation 1,

3[tex]l_{1}[/tex] + [tex]l_{2}[/tex] = 36

⇒  [tex]l_{2}[/tex] = 36 - 3[tex]l_{1}[/tex]  .............. (3)

From equation 2,

[tex]l_{1}[/tex] + 3[tex]l_{2}[/tex] = 24 ..................(4)

substitute equation the value of [tex]l_{2}[/tex] in 3 into equation 4,

[tex]l_{1}[/tex] + 3(36 - 3

[tex]l_{1}[/tex] + 108 - 9

108 -8[tex]l_{1}[/tex] = 24

108 - 24 = 8[tex]l_{1}[/tex]

⇒     [tex]l_{1}[/tex] = 10.5

Substitute the value of [tex]l_{1}[/tex] in equation 4,

[tex]l_{1}[/tex] + 3[tex]l_{2}[/tex] = 24

10.5 + 3[tex]l_{2}[/tex] = 24

3[tex]l_{2}[/tex] = 24 - 10.5

[tex]l_{2}[/tex] = 4.5

Thus,    [tex]l_{1}[/tex] = 10.5Km and [tex]l_{2}[/tex] = 4.5Km.

The length of the first path is 10.5Km, and the length of the second path is 4.5Km.

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