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

Explanation

The time between 2 mp and 3 pm =1 hr =60 min.
According to given condition
`60-t=(t^(2))/(4)-3`
`implies4t+t^(2)-12=240`
`impliest^(2)+4t-252=0`
`impliest^(2)+(18-14)t-252=0`
`impliest^(2)+18t-14t-252=0`
`impliest(t+18)-14(t+18)=0`
`implies(t+18)(t-14)=0`
`impliest+18=0ort-14=0`
`impliest=-18ort=14`
But t=-18 is not possible.
`because` The requried value of t = 14 min.