A 24hr digital hour digital clock is gaining three minutes every hour. If you set it to the correct time at 6p.m. on a Saturday, when will it show the correct time again?
24 * 3 = 72 minutes lost each day
24 * 60 = 1440 minutes per day
1440/72 = 20 days gained.
Take it from there.
it takes 20 hr to gain an hour
so, in 24 * 20 hr it will show the correct time
Since the digital clock is gaining three minutes every hour, it gains a total of 3 minutes every 60 minutes. This means it gains 1 minute every 20 minutes.
To determine when the clock will show the correct time again, we need to find the smallest multiple of 20 that represents the total minutes gained since 6 p.m. on a Saturday.
From 6 p.m. to 12 a.m., which is 6 hours, the clock gains a total of 6 x 3 = 18 minutes.
From 12 a.m. to 6 p.m. the next day, which is 18 hours, the clock gains a total of 18 x 3 = 54 minutes.
Therefore, from 6 p.m. on Saturday to 6 p.m. on Sunday, the clock gains a total of 18 minutes + 54 minutes = 72 minutes.
The smallest multiple of 20 that is greater than or equal to 72 is 4 x 20 = 80.
This means the clock will show the correct time again after 80 minutes.
Adding 80 minutes to 6 p.m. on Sunday, the correct time will be shown at 7:20 p.m. on Sunday.
To solve this problem, we need to calculate the total time it will take for the clock to show the correct time again.
The clock gains three minutes every hour. So, in one hour, it gains 3 minutes.
Since the clock is always running and gaining time, we can say that it takes 20 hours for the clock to gain one additional hour (60 minutes ÷ 3 minutes gained per hour = 20 hours).
Now, let's calculate how many additional hours the clock will gain until it shows the correct time again.
The clock shows the correct time at 6 p.m. on Saturday. We need to find out when it will show the correct time again.
There are 24 hours in a day, so 24 hours after 6 p.m. is 6 p.m. the next day. This means the clock will gain one additional hour in that time.
Since the clock gains one additional hour in 20 hours, we can calculate how many times it will gain one additional hour in 24 hours.
24 hours ÷ 20 hours = 1.2 additional hours gained.
Therefore, it will take the clock 1.2 days or approximately 1 day and 4 hours for it to show the correct time again.
So, if you set the clock to the correct time at 6 p.m. on a Saturday, it will show the correct time again at approximately 10 p.m. on a Sunday.