An 24hour digital clock is gaining three minutes every hour .If you set it to the correct time at 6 p.m.on Saturday,when will it show the correct time again? Answer must be in full form
oops 480 hours - 20 days
it must gain 24 hours.
3 minutes is 1/20 hour
24/(1/20) = 240 hours = 10 days
Well, it sounds like this clock likes to have its own little time party every hour, gaining three minutes. But let's see when it will finally decide to get back on track and show the correct time again.
From 6 p.m. on Saturday, if the clock is gaining three minutes every hour, it will take 20 hours for it to gain a full hour (since 60 minutes divided by 3 minutes is 20). So, after 20 hours from 6 p.m. on Saturday, the clock will show the incorrect time again.
Now, let's do the math. 20 hours later from 6 p.m. on Saturday would be 2 p.m. on Sunday. But hold your laughter, because the clock still needs to catch up the extra 3 minutes it gains every hour.
Since the clock gains 3 minutes every hour, it will take a full 60 minutes divided by 3 minutes, which is 20 times, to catch up on those extra 3 minutes. So, let's add 20 minutes to 2 p.m. on Sunday.
Drumroll, please! The clock will finally show the correct time again at 2:20 p.m. on Sunday. That's when it will stop clowning around and get itself together.
Since the clock gains three minutes every hour, it will gain 60 minutes in 20 hours (20 x 3 = 60). This means that the clock will show an extra one hour for every 20 hours that pass.
In order to determine when the clock will show the correct time again, we need to find out how many sets of 20 hours will pass until the extra one hour adds up to a full 24 hours, which corresponds to one day.
To calculate this, we can divide 24 by 1, which gives us 24 sets of 20 hours. Therefore, it will take 24 sets of 20 hours for the clock to show the correct time again.
Since each set of 20 hours is equivalent to 20 hours, we can multiply 24 by 20 to find the total number of hours it will take for the clock to show the correct time again.
24 x 20 = 480
Therefore, it will take 480 hours for the clock to show the correct time again.
If we convert this to days, we can divide 480 by 24, which gives us:
480 / 24 = 20
Thus, it will take 20 days for the clock to show the correct time again.
To find out when the clock will show the correct time again, we need to determine how much time it gains in a full day.
We know that the clock gains three minutes every hour. Therefore, in twenty-four hours (a full day), it gains 3 minutes/hour x 24 hours = 72 minutes.
This means that the clock gains 72 minutes each day compared to the correct time. Since there are 60 minutes in an hour, we can convert the 72 minutes to hours by dividing it by 60: 72 minutes / 60 minutes = 1.2 hours.
Therefore, each day, the clock is getting 1.2 hours further ahead of the correct time.
Now, let's determine how many days it will take for the clock to show the correct time again.
Since we set the clock to the correct time at 6 p.m. on Saturday, we need to consider that it gains 1.2 hours each day. So, at 6 p.m. on Sunday, the clock will be 1.2 hours ahead of the correct time again.
We can continue this process until the clock shows the correct time. Here's the breakdown:
- Saturday, 6 p.m. (correct time)
- Sunday, 6 p.m. (1.2 hours ahead of the correct time)
- Monday, 6 p.m. (2.4 hours ahead of the correct time)
- Tuesday, 6 p.m. (3.6 hours ahead of the correct time)
- Wednesday, 6 p.m. (4.8 hours ahead of the correct time)
- Thursday, 6 p.m. (6 hours ahead of the correct time)
- Friday, 6 p.m. (7.2 hours ahead of the correct time)
- Saturday, 6 p.m. (8.4 hours ahead of the correct time)
- Sunday, 6 p.m. (9.6 hours ahead of the correct time)
- Monday, 6 p.m. (10.8 hours ahead of the correct time)
- Tuesday, 6 p.m. (12 hours ahead of the correct time)
Therefore, the clock will show the correct time again on Tuesday at 6 p.m.