Question

Madison leaves her house and bikes north at a constant speed of 10 miles per hour. If her dad leaves the same house two hours later, driving north at a constant speed of 15 miles per hour, how long will it take him, in hours, to reach Madison?

Answer 1

6 hours later (based on Madison's time 0), they will see each other.

Explanation:

Let me write down two equations being equal to the other:

(1) for Madison: `Speed*time=`Distance In other words: `10*t=Distance`

(2) for her father: `15*(t-2)=`Distance

Why (t-2)? Because her father started his journey 2 hours later than Madison.

Now `10*t=15*(t-2)`

`10*t=15*t-30`

`30=(15-10)*t`

`30=5*t`

and `t=6` hours

6 hours later (just after Madison hit the road), they will see each other.