Question

A clock has an hour hand, minute hand, and second hand that measure 4 inches, 5
inches, and 6 inches, respectively. Find the distance traveled by the tip of each
hand in 20 minutes.

Answer 1

Arc length = radius × angle (in radians). In 20 minutes each hand turns a fraction of a full revolution:

- Second hand: period 1 min → 20 revs, angle = 20·2π = 40π. Distance = 6·40π = 240π in ≈ 753.98 in.
- Minute hand: period 60 min → 20/60 = 1/3 rev, angle = 2π/3. Distance = 5·(2π/3) = 10π/3 in ≈ 10.47 in.
- Hour hand: period 720 min → 20/720 = 1/36 rev, angle = 2π/36 = π/18. Distance = 4·(π/18) = 2π/9 in ≈ 0.698 in.