Question

if the hands of a clock coincide every 66 min (true time), then how much does the clock gain or lose every hour?

Answer 1

A clock that coincides every 66 minutes, instead of every 65 minutes, gains approximately 5 minutes and 27 seconds per hour.

Step-by-step explanation:

A student has asked about how much a clock will gain or lose every hour if the hands of the clock coincide every 66 minutes instead of the normal 65 minutes (true time). This question is rooted in mathematics and physics, specifically within the concept of time measurement and clock accuracy.

To find out how much time a clock gains or loses, we can compare the clock's time with the actual time. Since there are 60 minutes in an hour and the clock hands coincide every 66 minutes, the clock is gaining 6 minutes every 66 minutes.

In terms of hours, this gain can be calculated as (6/66) × 60 minutes, which simplifies to 5.4545 minutes per hour. This means that the clock gains approximately 5 minutes and 27 seconds every hour.