Question 345414: Two cars leave Cedar Lake, Indiana, at the same time, one heading due north, and the other one heading due east. After a few hours, they are 170 miles apart. The car traveling north had traveled 70 miles farther than the car traveling east.
(How far has each car traveled?) Hint: use pythagorean formula
Found 3 solutions by haileytucki, mananth, MathTherapy:
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! x^(2)+(x+70)^(2)=170^(2)
Squaring a number is the same as multiplying the number by itself (170*170). In this case, 170 squared is 28900.
x^(2)+(x+70)^(2)=28900
To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.
x^(2)+(x+70)^(2)-28900=0
Squaring an expression is the same as multiplying the expression by itself 2 times.
x^(2)+(x+70)(x+70)-28900=0
Multiply each term in the first group by each term in the second group using the FOIL method. FOIL stands for First Outer Inner Last, and is a method of multiplying two binomials. First, multiply the first two terms in each binomial group. Next, multiply the outer terms in each group, followed by the inner terms. Finally, multiply the last two terms in each group.
x^(2)+(x*x+x*70+70*x+70*70)-28900=0
Simplify the FOIL expression by multiplying and combining all like terms.
x^(2)+(x^(2)+140x+4900)-28900=0
Since x^(2) and x^(2) are like terms, add x^(2) to x^(2) to get 2x^(2).
2x^(2)+140x+4900-28900=0
Subtract 28900 from 4900 to get -24000.
2x^(2)+140x-24000=0
Factor out the GCF of 2 from each term in the polynomial.
2(x^(2))+2(70x)+2(-12000)=0
Factor out the GCF of 2 from 2x^(2)+140x-24000.
2(x^(2)+70x-12000)=0
In this problem 150*-80=-12000 and 150-80=70, so insert 150 as the right hand term of one factor and -80 as the right-hand term of the other factor.
2(x+150)(x-80)=0
Divide both sides of the equation by 2. Dividing 0 by any non-zero number is 0.
(x+150)(x-80)=0
Set each of the factors of the left-hand side of the equation equal to 0.
x+150=0_x-80=0
Since 150 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 150 from both sides.
x=-150_x-80=0
Set each of the factors of the left-hand side of the equation equal to 0.
x=-150_x-80=0
Since -80 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 80 to both sides.
x=-150_x=80
The complete solution is the set of the individual solutions.
x=-150,80
Answer= One has traveled 80 miles and the other 70 miles; they are 150 miles apart
Answer by mananth(16946)  (Show Source):
You can put this solution on YOUR website! let east bound car travel x
north bound car travels x+70 in the same time.
the distance between cars = 170 miles
....
x^2+(x+70)^2= 170^2
x^2+140x+4900 = 28900
x^2+140x+4900-28900 =0
x^2+140x-24000 = 0
x^2+240x-100x-24000=0
x(x+240)-100(x+240)=0
(x+240)(x-100)=0
x=100 OR x = -240. Ignore negative value.
east bound car has traveled 100 miles
north bound has traveled x+70 = 100+70 170 miles.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Two cars leave Cedar Lake, Indiana, at the same time, one heading due north, and the other one heading due east. After a few hours, they are 170 miles apart. The car traveling north had traveled 70 miles farther than the car traveling east.
(How far has each car traveled?) Hint: use pythagorean formula
Let the distance covered by the car traveling east be E
Since the car traveling north traveled 70 miles farther than the car traveling east, then the distance covered by the car traveling north is E + 70
Since one car traveled east while the other traveled north, their respective locations form a right triangle with the distance between them (170 miles) being the hypotenuse of the right triangle
We therefore have: 
 _____Factoring out GCF to reduce equation
(E + 150)(E - 80) = 0______Factoring trinomial
E = - 150 (ignore, as distance CANNOT be negative), or E = 80
E, or distance traveled by car heading east = 
E + 70, or distance traveled by car heading north = (80 + 70) = 
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