Problem:
Driving at a constant speed, Sharon usually takes 180 minutes to drive from her house to her mother's house. One day Sharon begins the drive at her usual speed, but after driving of the way, she hits a bad snowstorm and reduces her speed by 20 miles per hour. This time the trip takes her a total of 276 minutes. How many miles is the drive from Sharon's house to her mother's house?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the requested distance in miles, and suppose that Sharon usually drives at speed in miles per hour. Then . The total time in hours for Sharon's trip with the snowstorm is then . Because , this reduces to
Solving for gives .
OR
The last of the drive takes minutes, which is hours. If is the original speed in miles per hour, then of the distance is both and . Setting these expressions equal and solving yields . Therefore the original speed is 45 miles per hour, and the requested distance is miles.
The problems on this page are the property of the MAA's American Mathematics Competitions