#### 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 $\frac{t^{2}}{4}$ minutes. Find t.

14

Solution

At t minutes past 2 pm, the time need by minute hand to show 3 pm = 60 – t

According to question, it is given that (60 – t) is equal to 3 minutes less than $\frac{t^{2}}{4}$
$60-t=\frac{t^{2}}{4}-3\\ 60-t=\frac{t^{2}-12}{4}\\ t^{2}-12=4(60-t)\\ t^{2}-12=240-4t\\ t^{2}+4t-12-240=0\\ t^{2}+4t-252=0\\ t^{2}+18t-14t-252=0\\ t(t+18)-14(t+18)=0\\ (t+18)(t-14)=0\\ t=-18,14\\$

Time can’t equal to negative term.

Hence t = 14 minutes