Question 30904
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:

{{{3X - 3Y = 96 }}}

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

{{{X = 2Y}}}
[recall that X is the fast car]

So we have the system:
{{{system(3X - 3Y = 96 ,X = 2Y)}}}

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

{{{3(2Y) - 3Y = 96}}}
{{{6Y - 3Y = 96}}}
{{{3Y = 96}}}
{{{Y = 32}}}

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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