# Car speed to catch up to another person word problem.

You leave the house traveling $60$ mph. After you have driven $25$ miles, your mother leaves the house traveling in the same direction. What speed must your mother travel to catch up to you $5$ hours after she leaves?

I am really confused how to approach this problem. So I was thinking of starting by making a proportion: $$\frac{60 \text{ miles}}{60 \text{ minutes}}=\frac{25 \text{ miles}}{x \text{ minutes}}$$ But I don't know if this is right or what do to from there. Step by step explanation please!

When your mother leaves the house, you have driven $25\text{ miles}$. Five hours after this time, you have driven $25\text{ miles} + 60\text{ mph}\cdot 5\text{ h} = 325 \text{ miles}$.
So your mother needs to drive $325\text{ miles}$ in the $5$ hours that she has to catch up. This gives her a speed of $$325\text{ miles}/5\text{ hours} = 65\text{ mph}.$$