The point of the minute hand on a church clock travels 180 cm faster than the point of the hour hand in one complete revolution. If the hour hand is 60 cm long how long is the minute hand?

Answer 1

I assume you meant to say, " ... travels 180 cm farther than ... "

let the distance to the point of the minute hand be r cm

In one hour the minute hand has gone around one rotation or 2πr
in one hour the 'hour hand' has gone (1/12)(2π60))
or 10π cm

so 2πr - 10π = 180
πr = 90 + 5π
r = (90+5π)/π cm or appr 33.6 cm

Strange! , in most clocks the minute hand is longer than the hour hand, but...

checking::
in 1 hour, the minute hand has turned 2π(33.6..) cm = 211.4159.. cm
in 1 hour, the hour has turned 1/12 of 2π(60) = 31.4159.. cm
difference = 211.4159.. - 31.4159.. = 180 cm
My answer fits your data , check your typing of the question.