Question

At t minutes past 2 pm, the time needed by the minute hand of a clock to show 3 pm was found to be 3 min less than t (square) /4 min. Find t

Answer 1

Given time needed by the minutes hand show (t2/4) – 3
Hence the quadratic equation becomes, (t2/4) – 3 = 60 – t
(t2 – 12)/4 = 60 – t
(t2 – 12) = 240 – 4 t
t2 – 12 – 240 + 4 t = 0
t2 + 4t – 252 = 0
t2 + 18t – 14t – 252 = 0
t(t + 18) – 14(t + 18) = 0
(t + 18)(t – 14) = 0
(t + 18) = 0 or (t – 14) = 0
∴ t = - 18 or t = 14
Since t cannot be negative, t = 14