A CLOCK IS SHOWING THE RIGHT TIME AT 1PM. AFTER THIS IT STARTED GAINING 20 MIN/HR.SO,WHEN THIS CLOCK SHOWS 6PM,WHAT IS ACTUAL TIME?
A table can be helpful:
Real time Clock time
(p.m.) (p.m)
1:00 1:00
2:00 2:20
3:00 3:40
4:00 5:00
5:00 6:20
Clock time:
We can see that the desired clock time of 6:00 occurs in the interval between 5:00 and 6:20. From 5:00 to 6:20 is an 80 minute gap, but from 5:00 to 6:00 is only a 60 minute gap. Thus 6:00 occurs 60/80 of the way between 5:00 and 6:20, or 3/4 of the way.
Real time:
Transfer this fraction to the corresponding real time interval of 4:00 to 5:00.
3/4 of the way from 4:00 to 5:00 gets us to a real time of 4:45 p.m., the answer.
let's make a chart, RT = real time, FT = false time
time expressed as an fraction number
since 20 minutes = 1/3 hour ....
RT - FT
1.0 1+1/3 = 4/3 --> 1:20
2.0 4/3+4/3 = 8/3 --> 2:40
3.0 12/3 = 4.0 --> 4:00
4.0 16/3 --> 5:20
5.0 20/3 --> 6:40
So the real time falls between 4:00 and 5:00
let's set up a ratio
4.0 -- 16/3
t ---- 6.0
5.0 -- 20/3
(t-4)/(6 - 16/3) = (5-4)/(20/3 - 16/3)
(t-4)/(2/3) = 1/(4/3)
t-4 = (2/3) / (4/3) = (2/3)(3/4) = 1/2
t = 4 + 1/2
t = 4:30
Go with Plumpycat's table, I started mine with the wrong time at 1:00 , DUH
here is an easy way
80 false minutes = 60 reals
at 6:00 false times , 300 false minutes have passed
80/300 = 60/x
80x = 18000
x = 225 real minutes = 3 hours and 45 minutes
add that to 1:00 ----> 4:45 pm
To determine the actual time when the clock shows 6 PM, we need to take into account the time it started gaining 20 minutes per hour. Let's break down the steps to find the actual time:
1. Identify the time difference between 1 PM (when the clock was showing the correct time) and 6 PM (the time when we want to know the actual time).
The time difference is 5 hours since 6 PM is 5 hours after 1 PM.
2. Calculate the accumulated time gained by the clock during this 5-hour period.
The clock gains 20 minutes per hour, so in 5 hours, it would have gained: 5 hours * 20 minutes/hour = 100 minutes.
3. Subtract the accumulated gained time from the clock's displayed time at 6 PM to find the actual time.
Since the clock shows 6 PM, we subtract the gained time of 100 minutes from it: 6 PM - 100 minutes = 5:20 PM.
Therefore, when the clock shows 6 PM, the actual time is 5:20 PM.