On a bicycle, Stephanie rides for 2 hours and is 30 miles from her house. After riding for 5 hours, she is 66 miles away.

Question

On a bicycle, Stephanie rides for 2 hours and is 30 miles from her house. After riding for 5 hours, she is 66 miles away.

What is Stephanie's rate?______  miles per hour

How far away from her house did Stephanie start riding? _____ miles 

Write an equation to model this situation (use D

 for distance from her house in miles and H for hours).

___________

Answer 1

There's a BIG assumption in this problem which either the writer of the problem or you left out. That assumption is that Stephanie was riding at a constant speed the whole time. If that weren't the case, you can see that she could have started at home and ridden at two different average speeds.

Putting that aside, since we don't know how far she went on the first leg (because we don't yet know how far from home she was) work on the second leg. By subtraction,we can see that the second leg was 5-2=3 hours and covered 66-30=36 miles. 36 miles/3hours = 12 miles per hour. So that was her constant (or average) speed throughout the trip. The first leg took 2 hours. 2 hrs x 12 mi/hr = 24 miles.

If she traveled 24 miles and found herself 30 miles from home, then she must have started out 30-24=6 miles from home.

Best wishes!