Problem:
Gage skated each day for days and each day for days. How long would he have to skate the ninth day in order to average minutes of skating each day for the entire time?
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Solution:
In days, Gage skated for minutes, and in days he skated for minutes. So, in days he skated for minutes. To average minutes per day for days he must skate minutes, so he must skate minutes hours the ninth day.
For days Gage skated minutes under his desired average, and for days he skated minutes over his desired average. So, on the ninth day he needs to make up minutes. To do this, on the ninth day he must skate for minutes hours.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions