Question

At t minutes past 2 pm, the time needed by the minutes hand of a clock to show 3 pm was found to be 3 minutes less than `t^2/4` minutes. Find t.

Answer 1

We know that, the time between 2 pm to 3 pm = 1 h = 60 min

Given that, at f min 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^2/4` min

i.e., `t + (t^2/4 - 3)` = 60

⇒ 4t + t² – 12 = 240

⇒ t² + 4t – 252 = 0   

⇒ t² + 18t – 14t – 252 = 0   .....[By splitting the middle term]

⇒ t(t + 18) – 14(t + 18) = 0   ....[Since, time cannot be negative, so t ≠ – 18]

⇒ (t + 18)(t – 14) = 0

∴ t = 14 min

Hence, the required value of t is 14 min.