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

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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!

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$d_1 = 3 \cdot v$

$d_2 = 3 \cdot (v + 10)$

$d_1 + d_2 = 288 = 6 \cdot v + 30$

So $v = 43$ (and $53$)