Question

two watches are set correctly at 6pm on 29 lan 2004 one of the watches loses 7 min everyday while theother ganies 3 min everyday on which off the days in the nearest will both the watchses show 6O' clock at the same time
two watches are set correctly at 6pm on 29 lan 2004 one of the watches loses 7 min everyday while theother ganies 3 min everyday on which off the days in the nearest will both the watchses show 6O' clock at the same time

Answer 1

Answer:

1. It would take 1440 days for both clocks to show 6 o'clock once again.

Step-by-step explanation:

First thing's first, we need to convert everything into a single unit to simplify the solution.

For a clock to reach one full rotation, it would take 12 hours, or 720 minutes.

We need to find out how many additions and subtractions (or days) before the build up of 3 minutes reach a number that is divisible by 720, and the accumulated deduction of 7 minutes also reach a number that is exactly divisible by 720. An addition of a single “3 minute” each day (or 1440 minutes), and a single “7 minute” substraction for every 1440 minutes. This is to negate the effect that the addition and subtraction of minutes each day has on the two clocks.

We can ignore the accumulation of minutes of days because a single day (24 hours, 1440 minutes), is divisible by 720. No matter how many days (24 hours) later, a clock set at 6 o'clock will always show 6 o'clock.

This number of addition and substraction (or days) must be the same for the two, since they started at the same time. The least multiple of 3 that is divisible by 720 is 240.

240×3 minutes=720 minutes

However, this isn't the least multiple of 7 for it to reach a number that is divisible by 720.

240×7 minutes=1680 minutes

1680 minutes÷720=2.3333

If you calculate it, the least multiple of 7 for it to reach a number that is divisible by 720 is 1440.

1440×7 minutes=10,080 minutes

10,080 minutes÷720=14

This is also a multiple of 3 that will result in a number divisible by 720

1440×3=4,320 minutes

After 1440 additions of a single “3 minute” and subtractions of a single “7 minute”, the hands of the two clocks reach one full rotation (6 o'clock to 6 o'clock)

In other words, if the two clocks were set at the same time at 6 o’clock, it would take 1440 days for both clocks to show 6 o'clock once again.