Problem:
Jeremy's father drives him to school in rush hour traffic in minutes. One day there is no traffic, so his father can drive him miles per hour faster and gets him to school in minutes. How far in miles is it to school?
Answer Choices:
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E.
Solution:
Because the new time is of the original time, the new speed must be of the original speed. Then the additional miles per hour must be of the original speed, which is then . In minutes, Jeremy's father travels miles.
Let be Jeremy's original speed in miles per hour. Twenty minutes is of an hour and twelve minutes is of an hour. Then , so , and . Thus the distance to the school is miles.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions