# Two cars one $10$mph faster than other start at same point and travel in opposite directions.

In $3$ hours they are $288$ miles apart. Find the rate of both cars. I get wrong answer and can't figure out why.

Isn't $\frac{288}{3}=96$ the rate of the first car and $96+10= 106$ the rate of the second car?

Why do I have to do this $3(x+10)+3x=288$? Please help!

• If they're traveling in opposite directions, that means they're headed for each other. As such, the distance between them will be constantly decreasing over time, not increasing. – Grey Matters Apr 8 '17 at 2:28
• For some basic information about writing math on MSE see here, here, here and here. – user409521 Apr 8 '17 at 2:31
• @GreyMatters that is not true in this case, since the cars start from the same spot. So for instance, if they both start at the same spot, and one travels north and the other south, then the distance between them is surely increasing over time (unless they rounded the poles of the Earth, but I don't think that's the point here). – Dave Apr 8 '17 at 2:39
• "Isn't 288/3 the rate of the first car?" Um, no. Not at all. The first car did not not travel 288 miles. Both cars together traveled 288 miles. The first car, being slower traveled less than half that far. One way to is the sum of the speeds is 96mph so x+(x+10)=96 sa x=43 mph and the second is 53 mph. But I took shortcuts that will bite me if I'm not careful. – fleablood Apr 8 '17 at 5:52

$d_1 = 3 \cdot v$
$d_2 = 3 \cdot (v + 10)$
$d_1 + d_2 = 288 = 6 \cdot v + 30$
So $v = 43$ (and $53$)