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?

1 Answer
May 2, 2017

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.