# Kenna and Sariah are in an outdoor education camp in Waterton National Park, one of the activities is the orientation. Kenna's instructions are to walk to a direction of N20 ° W. Her average speed...

Kenna and Sariah are in an outdoor education camp in Waterton National Park, one of the activities is the orientation. Kenna's instructions are to walk to a direction of N20 ° W. Her average speed of walking on uneven ground is 3.5 km / h. Sariah's instructions are to walk to a direction of N33 ° E. The average walking speed is 1.0 km / h faster than Kenna because her career is covered in flat terrain towards a lake. How far will the girls be after 20 minutes of walk?

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N20 ° W would be 20 degrees past N on the way to W. Similarly N33 ° E would be 20 degrees past N on the way to E.

Let they starts together at the same time from point P.

Kenna travels towards N20 ° W at 3.5 km / h. Sariah travels towards N20 ° E at 4.5 km / h.

After 20 minutes, Kenna is at K, which is 3.5*20/60 = 1.1667 km away from P.

Similarly, after 20 minutes, Sariah should reach at S, which is 4.5*20/60 = 1.5 km away from P.

From the triangle PKS, side KS can be obtained from the cosine formula of triangles:

`c=sqrt(PK^2+PS^2-2PK*PScos53)`

`=sqrt((1.1667)^2+(1.5)^2-2*1.1667*1.5*0.6018)`

`=sqrt(1.5048)`

`=1.227 kM`

Therefore, after 20 minutes Kenna and Sariah will be 1.227 kM apart.