SOLUTION: Karen and David set out from home at the same time. Karen cycles due north 20km/h and David due east at 15km/h. FInd a) how far apart they are in 1 hour b)after how many minutes

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Question 1123733: Karen and David set out from home at the same time. Karen cycles due north 20km/h and David due east at 15km/h. FInd
a) how far apart they are in 1 hour
b)after how many minutes they are 10km apart
c) the bearing of Karen from David at any time
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Karen and David set out from home at the same time.
Karen cycles due north 20km/h and David due east at 15km/h.
FInd
a) how far apart they are in 1 hour
their routes form a right triangle, the hypotenuse is the dist between them
h = sqrt%2820%5E2%2B15%5E2%29
h = 25 km after 1 hr
:
b)after how many minutes they are 10km apart
Change the speeds to km/min
20/60 = .33 km/min
15/60 = .25 km/min
let the t = time in min for them to be 10km apart
%28.33t%29%5E2+%2B+%28.25t%29%5E2+=+10%5E2
.1111t%5E2+%2B+.0625t%5E2+=+100
.1736t%5E2+=+100
t%5E2+=+100%2F.1736
t^2 = 576
t = sqrt%28576%29
t = 24 min, they are 10 mi apart
:
c) the bearing of Karen from David at any time
Find the angle (David's position) using the tangent tan(A) = 20%2F15 = 53 degrees
In relation to true north, 90-53 = 37 degrees,
the Bearing then 360 - 37 = 323 degrees is Karen from David