Two cars leave town, one driving north and the other east. They are 26 miles apart when one of them is 14 miles farther from town than the other. At that time, how far were they each from the town? Distance driven by the two cars: ___miles?

Question

gw2011 · Answer

Let x=Distance of one car
Let x+14=Distance of the other car

Since one car travels north and the other car travels east, then the 26 miles represents the hypoteneuse.

The formula to be used for this right triangle is: c^2=a^2+b^2

(26)^2=(x+14)^2+(x)^2
676=x^2+28x+196+x^2
676=2x^2+28x+196   Simplify this equation by dividing by 2 and you get:

338=x^2+14x+98
0=x^2+14x+98-338
0=x^2+14x-240
0=(x+24)(x-10)

x+24=0
x=-24  This cannot be the solution because it is negative

x-10=0
x=10
x+14=10+14=24

Therefore, one car is 10 miles away and the other car is 24 miles away