Question

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 .

Answer 1

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

Explanation:

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

i.e speed =
`(distance)/(time)`

⇒ time =
`(distance)/(speed)`

Let the length of first path be represented by
`l_(1)`, and that of the second path by
`l_(2)`.

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

So that:

`(l_(1) )/(4)` +
`(l_(2) )/(12)` = 3 ............... (1)

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

So that:

`(l_(1) )/(12)` +
`(_(2) )/(4)` = 2 ................. (2)

From equation 1,

3
`l_(1)` +
`l_(2)` = 36

⇒
`l_(2)` = 36 - 3
`l_(1)` .............. (3)

From equation 2,

`l_(1)` + 3
`l_(2)` = 24 ..................(4)

substitute equation the value of
`l_(2)` in 3 into equation 4,

`l_(1)` + 3(36 - 3

`l_(1)` + 108 - 9

108 -8
`l_(1)` = 24

108 - 24 = 8
`l_(1)`

⇒
`l_(1)` = 10.5

Substitute the value of
`l_(1)` in equation 4,

`l_(1)` + 3
`l_(2)` = 24

10.5 + 3
`l_(2)` = 24

3
`l_(2)` = 24 - 10.5

`l_(2)` = 4.5

Thus,
`l_(1)` = 10.5Km and
`l_(2)` = 4.5Km.

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

Answer 2

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

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.