SOLUTION: Two cars start together and travel in the same direction, one going twice as fast as the other. At the end of 3 hours, they are 96 miles apart. How fast is each car traveling?

Question 30904: Two cars start together and travel in the same direction, one going twice as fast as the other. At the end of 3 hours, they are 96 miles apart. How fast is each car traveling?
Found 2 solutions by aussie7us, mbarugel:
Answer by aussie7us(3) (Show Source): You can put this solution on YOUR website!
This can be solved algebrically. You have two equations.
1- where x is the speed of the first car, and y is the speed of the second (faster) car.
2- 96 is their distance away from each other, and the 3's stand for the hours. car X has traveled for three hours, and so has car Y.
Next work out the equation. You can use substitution.
distribute
then
add like terms
then
divide both sides by 9
so car x (slow car) is traveling at 10 and 2/3 miles an hour.
Now, plug the X value into equation 1
The fast car is travelling at 21 and 1/3 miles an hour.

You can also check your answer. Plug in both numbers into equation 2. You get
if this equation is true, then your answers are correct.
(it is true)
HOPE THIS HELPS!
Answer by mbarugel(146) (Show Source): You can put this solution on YOUR website!
Hello!
The previous solution you got for this question ("The fast car is travelling at 21 and 1/3 miles an hour", etc) is actually incorrect.
Let's call X to the the speed of the faster car, and Y to the speed of the other one, both measured in miles per hour. After 3 hours, the fast car has traveled a distance of 3X miles, and the slow car has traveled a distance of 3Y miles.
Now, since they are 96 miles apart, the equation that describes this is:

The other equation ("one going twice as fast as the other") is:

[recall that X is the fast car]
So we have the system:

Substituting the 2nd equation into the 1st one, we get:

So the slow car is traveling at 32 mph, and the fast car is traveling at 64 mph.

I hope this helps!
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