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

Answer 1

As per question the following equation can be formed,
$\frac{t^2}{4}-3=60-t$

$\Rightarrow t^2-12=240-4t$

$\Rightarrow t^2+4t-252=0$

$\Rightarrow t^2+18t-14t-252=0$

$\Rightarrow t(t+18)-14(t+18)=0$

$\Rightarrow (t+18)(t-14)=0$

$t=-18$ or $t=14$