MathDB

On a clock, there are two instants between

12

noon and

1 \,\mathrm{PM}

, when the hour hand and the minute hannd are at right angles. The difference in minutes between these two instants is written as

a + \dfrac{b}{c}

, where

a, b, c

are positive integers, with

b < c

and

b/c

in the reduced form. What is the value of

a+b+c

Problem Statement