Question

Sang Jae walks a certain distance due north and then the same distance plus a further 7 km due east. If the final distance from the starting point is 17 km, find the distances he walks north and south

Answer 1

8 Km towards north and 15 Km towards east.

Explanation:

On the paper we define directions as -

• East - towards right
• West - towards left
• North - towards up
• South - towards down

The figure below illustrates the movement of Sang Jae.

Let he walked x Km distance towards north.

Distance towards east will be x + 7 Km

Given that the distance from origin to the final point is 17 Km.

As the triangle OAC is right angle triangle so

`OA^(2) + AC^(2) = OC^(2)`

`x^(2) + (x +7)^(2) = 289`

`x^(2) + x^(2) + 14x^{} + 49 = 289`

`2x^(2) + 14x^{} - 240 = 0`

`x^(2) + 7x^{} - 120 = 0`

`x^(2) + 15x^{} - 8x^{} - 120 = 0`

`x^{} (x^{} +15) - 8^{} (x^{} +15)=0`

`(x^{} -8)(x^{} +15)=0`

`x^{} = -15, 8`

Eliminating the negative value we get x = 8 Km.

So, Sang walked towards north = 8 Km.

And towards East = 8 + 7 = 15 Km.