SOLUTION: Distance between ships: At noon, Ship A is 45 miles due south of Ship B and is sailing north at a rate of 8 miles per hour. Ship B is sailing east at a rate of 6 miles per hour. Wr

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Question 707037: Distance between ships: At noon, Ship A is 45 miles due south of Ship B and is sailing north at a rate of 8 miles per hour. Ship B is sailing east at a rate of 6 miles per hour. Write the distance (d) between ships as a function of the time (t), where t=0 represents noon.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Distance between ships: At noon,
Ship A is 45 miles due south of Ship B and is sailing north at a rate of 8 miles per hour.
Ship B is sailing east at a rate of 6 miles per hour.
Write the distance (d) between ships as a function of the time (t), where t=0 represents noon.
:
The is a Pythagoras problem; d = sqrt%28a%5E2%2Bb%5E2%29 where:
a = 6t (distance east)
b = (45-8t); distance north
d = distance between the two ships
:
Ref point, is the starting point of b when t=0 they are 45 mi apart
d = sqrt%28%286t%29%5E2+%2B+%2845-8t%29%5E2%29
FOIL (45-8t)(45-8t)
d = sqrt%2836t%5E2+%2B+2025-720t%2B64t%5E2%29
combine like terms
d = sqrt%28100t%5E2-720t%2B2025%29
:
Graphically, time on the x axis, distance on the y axis
+graph%28+300%2C+200%2C+-10%2C+20%2C+-20%2C+200%2C+sqrt%28100x%5E2-720x%2B2025%29%2C+107%29+
You can see after 14 hrs, they are about 107 mi apart (green line)