Question

At t minutes past 2 p.m., the time needed by the minute hand of a clock to show 3 p.m. was found to be 3 minutes less than $\frac{t^2}{4}$ minutes . Find t .

Answer 1

t minutes past 2, the time needed to show 3 is 60-t.

As per the question,

$60-t=\frac{t^2}{4}-3$

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

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

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

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

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

$t=-18,14$

Ignoring the negative value,

$t=14$