Try this beautiful problem from the PRMO, 2019 based on Lines and Angles.
On a clock, there are two instants between 12 noon and 1 pm when the hour hand and the minute hand are at right angles. the difference in minutes between these two instants written as a+ where a b c are positive integers with
and
in the reduced form. find a+b+c.
Lines
Algebra
Angles
Answer: is 51.
PRMO, 2019, Question 7
Higher Algebra by Hall and Knight
Minute hand turns 6 (in degrees) in 1 min and hour hand turns half (in degree) in 1 min
x min after 12 is 6x -=90 or 270 (in degrees) then x =16
or 49
Difference 32 then a+b+c=32+8+11=51.
Try this beautiful problem from the PRMO, 2019 based on Lines and Angles.
On a clock, there are two instants between 12 noon and 1 pm when the hour hand and the minute hand are at right angles. the difference in minutes between these two instants written as a+ where a b c are positive integers with
and
in the reduced form. find a+b+c.
Lines
Algebra
Angles
Answer: is 51.
PRMO, 2019, Question 7
Higher Algebra by Hall and Knight
Minute hand turns 6 (in degrees) in 1 min and hour hand turns half (in degree) in 1 min
x min after 12 is 6x -=90 or 270 (in degrees) then x =16
or 49
Difference 32 then a+b+c=32+8+11=51.