SOLUTION: Please help me solve this word problem. I am very confused and it is a new topic. If you could not only give me an answer, but also include steps it would be greatly appreciated.

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Question 305461: Please help me solve this word problem. I am very confused and it is a new topic. If you could not only give me an answer, but also include steps it would be greatly appreciated.
Boat x sails due south from a pier. Boat Y sails due west from the same pier at the same time. Both sail at a constant speed. Boat x is sailing 2 miles per hour faster than Boat y. After one hour they are 8 miles apart. What is the speed of boat x in miles per hour?
Found 2 solutions by richwmiller, stanbon:
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
Word problems are meant to confuse you.
Who in their right mind could imagine that a math student would be able to read and do math?
If one boat goes south and another boat goes west, how could you figure out the distance between them?
look at a map. or draw n on the top of your paper. s on the bottom w on the left side and e on the right side
start in the middle. draw a line going west
go back the starting point in the middle. draw a line going south.
now connect the two end points. label that part 8
What did you draw ? a circle, rectangle or triangle?
What is special about it?
look at the angle in the middle.
What is the formula for distance?
rate (speed) times time =distance
r*t=d
time we are told is one hour
t=1
boat x is going x mph for one hour
boat y is going y mph for 1 hour
x=y+2
distance =1*(y+2)
distance =1*y
y^2+(y+2)^2=8^2
why?
y is the speed of boat y
y+2 is the speed of boat x
You will solve the equation for y but the question asks for x so add 2 to y to get x
Have fun.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Boat x sails due south from a pier. Boat Y sails due west from the same pier at the same time. Both sail at a constant speed. Boat x is sailing 2 miles per hour faster than Boat y. After one hour they are 8 miles apart. What is the speed of boat x in miles per hour?
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Draw the picture on a coordinate system.
Let the starting point be (0,0)
Boat x DATA:
time = 1 hour: rate = r+2 mph ; distance = (r+2) miles
----------------
Boat y DATA:
time = 1 hour ; rate = r mph ; distance = r miles
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The distance between the boats is the length of the
hypotenuse of the right triangle formed by their
paths and the distance between their positions.
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Equation:
r^2 + (r+2)^2 = 8^2
r^2 + r^2 + 4r + 4 = 64
2r^2 + 4r -60 = 0
r^2 + 2r - 30 = 0
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Using Quadratic Formula:
r = [-2 +- sqrt(4-4*-30)]/2
r = [-2 +- sqrt(124)]/2
r = [-2 +- 2sqrt(31)]/2
Positive solution:
r = -1 + sqrt(31)
r = 4.57 mph
r+2 = 6.57 mph
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Cheers,
Stan H.
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