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Question

can you please answer this question and maybe explain

two boats leave san diego at the same time. one boat sails due north and the other due west. when they are 10 miles apart, the boat traveling north has sailed 2 miles farther than the boat sailing west. find the distance each boat has traveled.

Answer 1

This should form a right-angled triangle.

The hypotenuse (longest side) should be 10 miles.
The distance of the boat travelling west should be x miles.
The distance of the boat travelling north should be x + 2 miles.

With that, try Pythagoras or some other method of finding x. Once you find x, you can find the distances of each boat.

Answer 2

Let the distance the boat sailing west travelled be x miles. Then the boat travelling north travelled x+2 miles. Using the Pythagorean theorem,

x^2 + (x + 2)^2 = 10^2
x^2 + x^2 + 4x + 4 = 100
2x^2 + 4x - 96 = 0
x^2 + 2x - 48 = 0
(x - 6)(x + 8) = 0
x = 6 or x = -8.

So the boat sailing west sailed 6 miles, and the boat sailing north sailed 8 miles.

Answer 3

its a right triangle!

let a = x = traveled by a boat sailing west.
b = x + 2 = traveled by a boat sailing north
c = 10 miles

a^2 + b^2 = c^2
x^2 + (x+2)^2 = 10^2
x^2 + x^2 + 4x + 4 = 100
2x^2 + 4x = 96
x^2 + 2x = 48; 48 = 8 x 6 = 2 x 2 x 2 x 2 x 3
x^2 + 2x - 48 = 0
(x + 8)(x - 6) = 0
x = -8; x = 6. note: there are no negative distances...

therefore, boat sailing west traveled 6 miles; boat sailing north traveled 8 miles....

Answer 4

This question you have to use pyth ther(sorry,forgot how to spell it.)since 1 boat is traveling north and another boath is traveling west,they will form a right-angle between them.so since they are 10 miles apart,let x be the distance of the boat that is traveling to the west.

so the boat traveling to north is 2 miles farther than the boat sailing west,the distance traveled is x+2.so they will form a triangle.Imagine it in your mind.so 10 square=(x+2) square + x square.

100=(x+2)(x+2) + x square.
100=x square + 4x + 4 + x square.
100= 2x square + 4x + 4.
2x square + 4x - 96=0
x square + 2x - 48=0.
so,now you factorize it.
it will become (x+8)(x-6)
so x is -8 or 6.
But you have to reject x=-8 as distance cannot negative.
so since x is 6,
x+2=8.
The boat traveling north traveled 8 miles and the boat traveling west traveled 6 miles.This is a secondary 2 question i believe.

Answer 5

Let a and b be the distances traveled due north and due west by the two boats.

a = b + 2 as given and

a^2 + b^2 = 10^2 (right angled triangle - hypotenuse)

So, b^ + 4b + 4 + b^2 = 100

2b^2 + 4b = 96

b^2 + 2b = 48

or b^2 + 2b - 48 = 0

The roots of this equation are (b - 6) (b + 8)

So b = 6 or -8

Ignoring the negative value, b = 6 and a = 8 miles