SOLUTION: two cyclists depart from the same point one travels due east at 18 km/hr while the other travels North-west at 20 km/hr how long will it be bore they are 80 km apart
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Question 972986: two cyclists depart from the same point one travels due east at 18 km/hr while the other travels North-west at 20 km/hr how long will it be bore they are 80 km apart Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! two cyclists depart from the same point one travels due east at 18 km/hr while the other travels North-west at 20 km/hr
how long will it be before they are 80 km apart
:
let t = time in hrs for them to be 80 km apart
then
18t = the distance traveled by the 1st cyclist
20t = the distance traveled by the 2nd
:
The angle between the two paths: 45 + 90 = 135 degrees
Draw this out as a triangle, the side opposite 135 degrees is 80 km
:
Use the law of cosines: b^2 + c^2 - 2(bc)cos(A) = a^2; where:
a = 80
b = 18t
c = 20t
Angle A = 135 degrees
:
(18t)^2 + (20t)^2 - 2(18t*20t)Cos(135) = 80^2
324t^2 + 400t^2 - 2(360t^2)*-.707 = 6400
724t^2 - (-509.117t^2) = 6400
724t^2 + 509.117t^2 = 6400
1233t^2 = 6400
t^2 =
t^2 = 5.2
t =
t = 2.28 hrs they will be 80 km apart
