Question 814982: Two vehicles leave the same corner at the same time and travel at a right angle to each other. One vehicle travels 3 kilometers an hour faster than the other. If after one hour the vehicles are 15 kilometers apart, find the rate of each vehicle.
Found 2 solutions by FightinBlueHens, josmiceli:
Answer by FightinBlueHens(27)   (Show Source):
You can put this solution on YOUR website! Imagine one Car is going north, and one car is going east.
Let the speed of the car going north y represented by y, (y kilometes/hr)and the speed of the car going east be represented by y+3 (y+3 kilometers/hr).
By the end of one hour they are 15 kilometers apart, so you have a right triangle, and you can measeure how far each car traveled from it's starting poing by using the Pythagorean Theorem that says the square of the hypotenuse is equal to the sum of the square of the sides(a^2 + b^2 = c^2).
Let the distance of the car traveling north be represented by a (after 1 hour), and the distance of the car going east be represented by b (after 1 hour). The hypotenuse, or the diagonal line, which is the total distance between the 2 cars after one hour can be represented by c.
a^2 + b^2 = c^2
y^2 + (y+3)^2 = 15^2 Replace the variables of the equation with the vaariables that you have decided will represent the numbers you want to work with.
y^2+(y^2+6y+9) = 225 Distrubute for the second term, and square 15.
y^2+y^2 +6y+9-225=0 Bring 225 to the left side to have all terms on one side to solve the problem.
2y^2+6y-216=0 Simplify the problem.
y^2+3y-108=0 Divide both sides by 2.
(y )(y ) Now you have to factor, so find the factors of 108. They are: (2, 54), (4, 27), (3, 36), (6, 18), (9, 12)
Which of these factors, when multiplied give you -108 (all of them) AND when added give you 3?
(y 3)(y 12) These factors are 3 and 12. Now figure out what + or - symbols you need to solve the problem and where they go.
(y-3)(y+12)=0
y-3=0 Divide both sides by (y+12)
y=3. Add 3 to both sides to find out one possible answer.
y+12=0 Solve for the other answer by dividing both sides of (y-3)(y+12)=0 by (y-3)
y=-12 Subtract 12 from both sides to get the other answer.
The only answer that makes sense is y=3 because it is a positive speed.
So the car going north was going 3 km/hr, and the car going east was going 6 km/hr.
Answer by josmiceli(19441)  (Show Source):
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