Question

The outside temperature at midnight today in Polina’s hometown was 18 degrees Fahrenheit. The temperature increases by 1.2 degrees Fahrenheit each hour over the next 15 hours. Polina’s school does not send students outside for recess if the outside temperature is 32 degrees Fahrenheit or lower. Recess at her school always starts on the half hour or hour. Which statement is true about recess at Polina’s school?
Only students who have recess at 11:00 a.m. or later may go outside.
Only students who have recess at 11:30 a.m. or later may go outside.
Only students who have recess at 12:00 p.m. or later may go outside.
Only students who have recess at 12:30 p.m. or later may go outside.

Answer 1

Temperature after t hours: T = 18 + 1.2t.
Solve 18 + 1.2t > 32 → 1.2t > 14 → t > 11.666... hours = 11 hours 40 minutes (11:40 a.m.).

Since recess starts on the hour or half hour, the first recess time after 11:40 a.m. is 12:00 p.m. (at 12:00, T = 18 + 1.2·12 = 32.4°F). Therefore only students who have recess at 12:00 p.m. or later may go outside.