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

We know that the time between 2 pm to 3pm `1h=60` min
Given that at `t` min past 2pm the time needed by the min hand of a clock to show 3 pm was found to be 3 minless than `(t^(2))/4` min i.e.
`t+((t^(2))/4-3)=60`
`implies 4t+t^(2)-12=240`
`impliest^(2)+4t-252=0`
`impliest^(2)+18t-14t-252=0`
`implies t^(2)+18t-14t-252=0` [by splitting the middle term]
`implies t(t+18)-14(t+18)=0` [since, time cannot be neative so `t!=-18`]
`implies (t+18)(t-14)=0`
`:. t=14` min
Hence the required value to `t` is 14 min.