SOLUTION: Two cargo boats leave the same port at the same time. The direction of one boat is at an angle of 30 degrees to the other. If the ratio of the speed of the first boat to the second

Algebra.Com
Question 1125459: Two cargo boats leave the same port at the same time. The direction of one boat is at an angle of 30 degrees to the other. If the ratio of the speed of the first boat to the second is sqrt 3 over 2, and if the second boat travels at 18km/h, how far apart, in km, are they at the end of 5 hours?
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
Two cargo boats leave the same port at the same time.
The direction of one boat is at an angle of 30 degrees to the other.
If the ratio of the speed of the first boat to the second is sqrt 3 over 2, and if the second boat travels at 18km/h, how far apart, in km, are they at the end of 5 hours?
:
Find the speed of the 1st boat (s)
=
cross multiply

s =
s = 15.6 km/h is the speed of the 2nd boat
:
Find the distance each has traveled in 5 hrs
5*15.6 = 78 km traveled by the 1st boat
5*18 = 90 km by the 2nd boat
:
The distance between the boat is the side (a) opposite the 30 degree angle (A)
Use the law of cosines: a^2 = b^2 + c2 - 2bc*Cos(a),where
b = 78
c = 90

a^2 = 6084 + 8100 - 2(7020)*.866
Do the math
a =
a = 45 km apart in 5 hrs
Answer by MathTherapy(10550)   (Show Source): You can put this solution on YOUR website!
Two cargo boats leave the same port at the same time. The direction of one boat is at an angle of 30 degrees to the other. If the ratio of the speed of the first boat to the second is sqrt 3 over 2, and if the second boat travels at 18km/h, how far apart, in km, are they at the end of 5 hours?
Let speed of 1st boat be S

Then we get the following: 

 ------- Cross-multiplying

S, or speed of 1st boat = 

We then get: 	Distance traveled by 1st boat in 5 hours: 

               

Distance traveled by 2nd boat in 5 hours: 5(18) = 90 km



The side opposite the 30o angle represents the distance between the boats after 5 hours

Therefore, with 2 SIDES and an INCLUDED ANGLE (SAS), we use the law of cosines.

Let the side opposite the 30o angle (A) be a

Then we get:   

                     

                    

              

             

             

             

             Distance the boats are apart, or 

             OR

               

             

             

             Distance the boats are apart, or  

RELATED QUESTIONS


Two cargo boats leave the same port at the same time. The direction of one boat is at an... (answered by MathLover1)

Two boats leave the port at the same time. The first boat travels due east at 14 mph, and  (answered by jojo14344)

I have have been struggling with this for half of the day.  I would appreciate any... (answered by josmiceli)

two boats leave the same port at the same time, the first boat heads due north at 15... (answered by Alan3354)

Two boats leave a dock at the same time and at a 90° angle from each other.
After 3... (answered by rfer)

Please help me with this problem: Two boats leave the buoy at the same time. One of the... (answered by ankor@dixie-net.com)

Two boats leave the dock at the same time going in the same direction.
The first boat... (answered by mananth)

Two boats leave a harbour at the same time and head out at an angle of 35o to each other.  (answered by ewatrrr,ikleyn)

Two boats leave the harbour at the same time. Boat A travels at 32km/h on a bearing of... (answered by lwsshak3)