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 min 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 + t^2 - 12` = 240

⇒ `t^2 + 4t - 252` = 0   

⇒ `t^2 + 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 off is 14 min.