jmc

Question

An airplane climbs 100 feet during the first second after takeoff. In each succeeding second it climbs 100 feet more than it climbed during the previous second. How many seconds does it take for the plane to reach an altitude of 12,000 feet above its takeoff height?

Accepted Answer

After t seconds, the airplane's altitude (in feet) is 100 + 200 + + 100t = 100(1 + 2 + + t) = 100 t(t + 1)/2 = 50t(t + 1). Thus, we want to find the smallest t such that 50t(t + 1) 12000. Dividing both sides by 50, we get t(t + 1) 240. Since 15 16 = 240, the smallest such t is t = 15.