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?

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.

To find the length of the minute hand, we first need to determine the speed at which each hand moves.

The distance traveled by a point on the clock is directly proportional to the radius of the hand. So, let's call the speed of the hour hand Vh (in cm/minute) and the speed of the minute hand Vm (in cm/minute).

We know that the length of the hour hand is 60 cm, so in one revolution (12 hours), the distance traveled by a point on the hour hand would be the circumference of a circle with a radius of 60 cm, which is 2π * 60 = 120π cm.

Similarly, in one revolution of the minute hand, the distance traveled by a point on the minute hand would be the circumference of a circle with a radius that we need to find. Let's call this radius R (in cm). So, the distance traveled by a point on the minute hand would be 2π * R = 2πR cm.

The problem states that the point of the minute hand travels 180 cm faster than the point of the hour hand in one complete revolution. So, we can set up the following equation:

2πR = 120π + 180

Now, let's solve for R:

2πR = 120π + 180
R = (120π + 180) / (2π)
R = 60 + 90 / π
R ≈ 60 + 28.65
R ≈ 88.65 cm

Therefore, the length of the minute hand is approximately 88.65 cm.