A young equestrian loved to ride her horse all day long, dreaming of the day she would ride in the Kentucky Derby. One day in early April, she left home at 10:00 am and rode her stallion at a nice, steady 10 miles per hour away from her house. At noon a call came in from the Derby saying she was in! Her father immediately jumped on his scooter to try and track her down and tell her the good news.

Riding at a breezy 15 miles per hour, after how many hours on the scooter will her father catch up to her?

Question

A young equestrian loved to ride her horse all day long, dreaming of the day she would ride in the Kentucky Derby. One day in early April, she left home at 10:00 am and rode her stallion at a nice, steady 10 miles per hour away from her house. At noon a call came in from the Derby saying she was in! Her father immediately jumped on his scooter to try and track her down and tell her the good news. 

Riding at a breezy 15 miles per hour, after how many hours on the scooter will her father catch up to her?

mathstudent55 · Answer

If you think of how much distance each one moves at the end of each hour, you can figure this out without equations.

mathstudent55 · Answer

Fill in the table below.

Time     Position of Girl        Position of Father
0 hr            0 miles                    0 miles
1 hr
2 hrs
3 hrs
4 hrs
5 hrs
6 hrs

mathstudent55 · Answer

Have you tried it?

mathmale · Answer

The young person will have been riding at 10 mph for 2 hours when her father begins riding at 15 mph.  Derive two linear functions in t from this info.  Set these functions equal to each other and solve for time, t.