Question

There are two different clocks in Wendy's house, one is 20 minutes faster in a day, and the other is 30 minutes slower in a day. If they are set to be the correct time now, how many days later will they both show the correct time?

Answer 1

The answer is below

Explanation:

For the first clock that is 20 minutes faster in a day, that means it is
`(20\ min)/(60\ min/hr)=(1)/(3)hr` faster every day. For it to show the correct time, the clock should be 24 hours faster.

Since 1 day = 1/3 hr faster

x days = 24 hr faster

Let x number of days be required to be 24 hr faster. To find x we use the formula:

`x=(24 \ hr* 1\ day)/((1)/(3)hr ) \\x=72\ days`

For the second clock that is 30 minutes slower in a day, that means it is
`(30\ min)/(60\ min/hr)=(1)/(2)hr` faster every day. For it to show the correct time, the clock should be 24 hours slower.

Since 1 day = 1/2 hr slower

y days = 24 hr faster

Let x number of days be required to be 24 hr slower. To find x we use the formula:

`y=(24 \ hr* 1\ day)/((1)/(2)hr ) \\y=48\ days`