SOLUTION: Two fishing boats depart a harbor at the same time, traveling east, the other south. The eastbound boat travels at a speed 3mph faster than the southbound boat. After two hours the

Question 566328: Two fishing boats depart a harbor at the same time, traveling east, the other south. The eastbound boat travels at a speed 3mph faster than the southbound boat. After two hours the boats are 30 miles apart. Find the speed of the southbound boat.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two fishing boats depart a harbor at the same time, traveling east, the other south.
The eastbound boat travels at a speed 3mph faster than the southbound boat.
After two hours the boats are 30 miles apart.
Find the speed of the southbound boat.
:
Let s = speed of the southbound boat
then
(s+3) = speed of the eastbound boat
:
Dist = speed * time, therefore:
:
2s = dist traveled by the southbound boat
2(s+3) = (2s+6); dist traveled by the east bound
:
This is a right triangle problem, the distance between the boats is the hypotenuse
a^2 + b^2 = c^2, where
a = 2s
b = (2s+6)
c = 30
:
(2s^2) + (2s+6)^2 = 30^2
4s^2 + 4s^2 + 24s + 36 = 900
8s^2 + 24s + 36 - 900 = 0
8s^2 + 24s - 864 = 0
simplify, divide by 8
s^2 + 3s - 108 = 0
Factors to
(s+12)(s-9) = 0
the positive solution
s = 9 mph, the speed of the southbound boat
:
:
Check this on a calc,
southbound boat traveled 2*9 = 18 mi
eastbound boat traveled 2*12 = 24 mi
:
enter results: 30
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