Question

Gerry is to memorize 150 terms for a quiz. If the rate by which the number of terms Gerry memorizes is directly proportional to the number of terms already memorized and the number of remaining terms; and that initially Gerry knows 5 terms and 20 terms 5 minutes later. At what time is he half done?

Answer 1

$v=kx$

$k5(5-0)=15$

$k=15/25=3/5$

$3/5\int_0^{75}dt=3/5\cdot 75=45$

Answer: Gerry is half done at 45 minutes